The addition \left(\overrightarrow{A}+\overrightarrow{B}\right) ( A <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> + B <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> ) of the following vectors A → = ( 15 , 3 , 2 ) a n d B → = ( − 5 , 2 , − 9 ) \overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right) A <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 1 5 , 3 , 2 ) a n d B <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( − 5 , 2 , − 9 ) is...

R → = ( 10 , 5 , − 7 ) \overrightarrow{R}=\left(10,5,-7\right) R <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 1 0 , 5 , − 7 )

R → = ( 20 , 5 , − 7 ) \overrightarrow{R}=\left(20,5,-7\right) R <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 2 0 , 5 , − 7 )

R → = ( 20 , 1 , 11 ) \overrightarrow{R}=\left(20,1,11\right) R <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 2 0 , 1 , 1 1 )

R → = ( 10 , 1 , 11 ) \overrightarrow{R}=\left(10,1,11\right) R <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 1 0 , 1 , 1 1 )

The subtraction ( A → − B → ) \left(\overrightarrow{A}-\overrightarrow{B}\right) ( A <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> − B <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> ) of the following vectors A → = ( 15 , 3 , 2 ) a n d B → = ( − 5 , 2 , − 9 ) \overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right) A <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 1 5 , 3 , 2 ) a n d B <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( − 5 , 2 , − 9 ) is...

R → = ( 20 , 1 , 11 ) \overrightarrow{R}=\left(20,1,11\right) R <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 2 0 , 1 , 1 1 )

R → = ( 10 , 5 , − 7 ) \overrightarrow{R}=\left(10,5,-7\right) R <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 1 0 , 5 , − 7 )

R → = ( 20 , 5 , − 7 ) \overrightarrow{R}=\left(20,5,-7\right) R <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 2 0 , 5 , − 7 )

R → = ( 10 , 1 , 11 ) \overrightarrow{R}=\left(10,1,11\right) R <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 1 0 , 1 , 1 1 )

Vector operations

Authored by Oscar Diaz

Physics

12th Grade

Used 9+ times

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The x-component of vector
$\overrightarrow{T}=27.73,\ \ \propto=43.84°,\ \ \beta=64.35°,\ \gamma=57.25°$ is...

$\approx$ 43.84

$\approx$ 12

$\approx$ 20

$\approx$ 27.73

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The z-component of vector
$\overrightarrow{M}=3i-2j+7k$ is....

-2

27.25°

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The magnitude of vector
$\overrightarrow{M}=3i-2j+7k$ is....

7.87

27.25°

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The y-component of vector
$\overrightarrow{T}=27.73,\ \ \propto=43.84°,\ \ \beta=64.35°,\ \gamma=57.25°$ is...

$\approx$ 12

$\approx$ 15

$\approx$ 20

$\approx$ 57.25

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The magnitude of vector
$\overrightarrow{K}=40i-12j+20k$ is....

2144

43.08

46.30

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The addition
$\left(\overrightarrow{A}+\overrightarrow{B}\right)$
of the following vectors $\overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right)$ is...

$\overrightarrow{R}=\left(10,5,-7\right)$

$\overrightarrow{R}=\left(20,5,-7\right)$

$\overrightarrow{R}=\left(20,1,11\right)$

$\overrightarrow{R}=\left(10,1,11\right)$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The subtraction
$\left(\overrightarrow{A}-\overrightarrow{B}\right)$
of the following vectors $\overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right)$ is...

$\overrightarrow{R}=\left(10,5,-7\right)$

$\overrightarrow{R}=\left(20,5,-7\right)$

$\overrightarrow{R}=\left(20,1,11\right)$

$\overrightarrow{R}=\left(10,1,11\right)$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The dot product
$\left(\overrightarrow{A}\cdot\overrightarrow{B}\right)$
of the following vectors $\overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right)$ is...

-51

-87

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Vector operations

The x-component of vector T→=27.73, ∝=43.84°, β=64.35°, γ=57.25°\overrightarrow{T}=27.73,\ \ \propto=43.84°,\ \ \beta=64.35°,\ \gamma=57.25°T=27.73, ∝=43.84°, β=64.35°, γ=57.25° is...

The z-component of vector M→=3i−2j+7k\overrightarrow{M}=3i-2j+7kM=3i−2j+7k is....

The magnitude of vector M→=3i−2j+7k\overrightarrow{M}=3i-2j+7kM=3i−2j+7k is....

The y-component of vector T→=27.73, ∝=43.84°, β=64.35°, γ=57.25°\overrightarrow{T}=27.73,\ \ \propto=43.84°,\ \ \beta=64.35°,\ \gamma=57.25°T=27.73, ∝=43.84°, β=64.35°, γ=57.25° is...

The magnitude of vector K→=40i−12j+20k\overrightarrow{K}=40i-12j+20kK=40i−12j+20k is....

The addition \left(\overrightarrow{A}+\overrightarrow{B}\right)(A+B) of the following vectors A→=(15, 3, 2) and B→=(−5, 2, −9)\overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right)A=(15, 3, 2) and B=(−5, 2, −9) is...

The subtraction (A→−B→)\left(\overrightarrow{A}-\overrightarrow{B}\right)(A−B) of the following vectors A→=(15, 3, 2) and B→=(−5, 2, −9)\overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right)A=(15, 3, 2) and B=(−5, 2, −9) is...

The dot product (A→⋅B→)\left(\overrightarrow{A}\cdot\overrightarrow{B}\right)(A⋅B) of the following vectors A→=(15, 3, 2) and B→=(−5, 2, −9)\overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right)A=(15, 3, 2) and B=(−5, 2, −9) is...

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The x-component of vector
$\overrightarrow{T}=27.73,\ \ \propto=43.84°,\ \ \beta=64.35°,\ \gamma=57.25°$ is...

The z-component of vector
$\overrightarrow{M}=3i-2j+7k$ is....

The magnitude of vector
$\overrightarrow{M}=3i-2j+7k$ is....

The y-component of vector
$\overrightarrow{T}=27.73,\ \ \propto=43.84°,\ \ \beta=64.35°,\ \gamma=57.25°$ is...

The magnitude of vector
$\overrightarrow{K}=40i-12j+20k$ is....

The addition
$\left(\overrightarrow{A}+\overrightarrow{B}\right)$
of the following vectors $\overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right)$ is...

The subtraction
$\left(\overrightarrow{A}-\overrightarrow{B}\right)$
of the following vectors $\overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right)$ is...

The dot product
$\left(\overrightarrow{A}\cdot\overrightarrow{B}\right)$
of the following vectors $\overrightarrow{A}=\left(15,\ 3,\ 2\right)\ \ \ and\ \ \ \overrightarrow{B}=\left(-5,\ 2,\ -9\right)$ is...