(ii) Find O E → \overrightarrow{OE} O E <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 4 a + 3 2 b \frac{1}{4}a+\frac{3}{2}b 4 1 a + 2 3 b

1 4 a − 2 b \frac{1}{4}a-2b 4 1 a − 2 b

(iii) Find C D → \overrightarrow{CD} C D <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 4 ( a − 2 b ) \frac{1}{4}\left(a-2b\right) 4 1 ( a − 2 b )

1 2 ( a + 2 b ) \frac{1}{2}\left(a+2b\right) 2 1 ( a + 2 b )

1 4 ( a + 2 b ) \frac{1}{4}\left(a+2b\right) 4 1 ( a + 2 b )

1 2 ( a − 2 b ) \frac{1}{2}\left(a-2b\right) 2 1 ( a − 2 b )

(ii) Find A C → \overrightarrow{AC} A C <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 3 ( b − a ) \frac{1}{3}\left(b-a\right) 3 1 ( b − a )

3 ( b − a ) 3\left(b-a\right) 3 ( b − a )

1 3 ( a − b ) \frac{1}{3}\left(a-b\right) 3 1 ( a − b )

1 3 ( a + b ) \frac{1}{3}\left(a+b\right) 3 1 ( a + b )

(iii) Find O C → \overrightarrow{OC} O C <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 3 ( 2 a + b ) \frac{1}{3}\left(2a+b\right) 3 1 ( 2 a + b )

3 ( 2 a + b ) 3\left(2a+b\right) 3 ( 2 a + b )

1 3 a + 1 3 b \frac{1}{3}a+\frac{1}{3}b 3 1 a + 3 1 b

2 3 a − 1 3 b \frac{2}{3}a-\frac{1}{3}b 3 2 a − 3 1 b

(i) Find P Q → \overrightarrow{PQ} P Q <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 ( 2 q − p ) 2\left(2q-p\right) 2 ( 2 q − p )

2 ( q − p ) 2\left(q-p\right) 2 ( q − p )

(ii) Find P X → \overrightarrow{PX} P X <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 3 ( 2 q − p ) \frac{2}{3}\left(2q-p\right) 3 2 ( 2 q − p )

2 ( 3 q − p ) 2\left(3q-p\right) 2 ( 3 q − p )

1 3 ( q − p ) \frac{1}{3}\left(q-p\right) 3 1 ( q − p )

2 3 q − 2 3 p \frac{2}{3}q-\frac{2}{3}p 3 2 q − 3 2 p

(iii) Find O X → \overrightarrow{OX} O X <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">

4 3 ( p + q ) \frac{4}{3}\left(p+q\right) 3 4 ( p + q )

4 3 ( p − q ) \frac{4}{3}\left(p-q\right) 3 4 ( p − q )

3 4 ( p + q ) \frac{3}{4}\left(p+q\right) 4 3 ( p + q )

(i) Find A B → \overrightarrow{AB} A 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">

1 2 ( a − b ) \frac{1}{2}\left(a-b\right) 2 1 ( a − b )

(ii) Find A D → \overrightarrow{AD} A D <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 ( a − b ) 2\left(a-b\right) 2 ( a − b )

(iii) Find C D → \overrightarrow{CD} C D <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 3 ( 4 b − a ) \frac{1}{3}\left(4b-a\right) 3 1 ( 4 b − a )

1 4 ( 3 b − a ) \frac{1}{4}\left(3b-a\right) 4 1 ( 3 b − a )

1 4 ( a − b ) \frac{1}{4}\left(a-b\right) 4 1 ( a − b )

(i) (a) Find A B → \overrightarrow{AB} A 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">

3 ( 2 b − a ) 3\left(2b-a\right) 3 ( 2 b − a )

3 ( 2 b − 2 a ) 3\left(2b-2a\right) 3 ( 2 b − 2 a )

− 6 b + 2 a -6b+2a − 6 b + 2 a

(i) (b) Find O D → \overrightarrow{OD} O D <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 ( a + b ) 2\left(a+b\right) 2 ( a + b )

2 ( a − b ) 2\left(a-b\right) 2 ( a − b )

(i) (c) Find B C → \overrightarrow{BC} B C <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">

6 ( 1 5 a − b ) 6\left(\frac{1}{5}a-b\right) 6 ( 5 1 a − b )

6 a − 1 5 b 6a-\frac{1}{5}b 6 a − 5 1 b

(ii) Find B E → \overrightarrow{BE} B E <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">

6 h ( 1 5 a − b ) 6h\left(\frac{1}{5}a-b\right) 6 h ( 5 1 a − b )

6 h ( 5 a − b ) 6h\left(5a-b\right) 6 h ( 5 a − b )

6 5 ( h a − b ) \frac{6}{5}\left(ha-b\right) 5 6 ( h a − b )

h ( 1 5 a + b ) h\left(\frac{1}{5}a+b\right) h ( 5 1 a + b )

Vectors in Mathematics

Authored by Gideon Mufumbi

Mathematics

11th - 12th Grade

CCSS covered

Used 19+ times

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16 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

(i) Find $\overrightarrow{OB}$

$a+2b$

$-a+2b$

$2a+b$

$2a-2b$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

(ii) Find $\overrightarrow{OE}$

$a+3b$

$\frac{1}{4}a-2b$

$\frac{1}{4}a+\frac{3}{2}b$

$b+4a$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

(iii) Find $\overrightarrow{CD}$

$\frac{1}{2}\left(a+2b\right)$

$\frac{1}{4}\left(a+2b\right)$

$\frac{1}{4}\left(a-2b\right)$

$\frac{1}{2}\left(a-2b\right)$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

(i) Find $\overrightarrow{AB}$

$a-b$

$a+b$

$-a-b$

$b-a$

(ii) Find $\overrightarrow{AC}$

$3\left(b-a\right)$

$\frac{1}{3}\left(b-a\right)$

$\frac{1}{3}\left(a-b\right)$

$\frac{1}{3}\left(a+b\right)$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

(iii) Find $\overrightarrow{OC}$

$\frac{1}{3}\left(2a+b\right)$

$3\left(2a+b\right)$

$\frac{1}{3}a+\frac{1}{3}b$

$\frac{2}{3}a-\frac{1}{3}b$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

(i) Find $\overrightarrow{PQ}$

$2q-4p$

$2\left(2q-p\right)$

$2\left(q-p\right)$

$p-2q$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

(ii) Find $\overrightarrow{PX}$

$2\left(3q-p\right)$

$\frac{1}{3}\left(q-p\right)$

$\frac{2}{3}q-\frac{2}{3}p$

$\frac{2}{3}\left(2q-p\right)$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

(iii) Find $\overrightarrow{OX}$

$\frac{4}{3}\left(p+q\right)$

$p+q$

$\frac{4}{3}\left(p-q\right)$

$\frac{3}{4}\left(p+q\right)$

10.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

(i) Find $\overrightarrow{AB}$

$\frac{1}{2}\left(a-b\right)$

$a+b$

$b-a$

$a-b$

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Vectors in Mathematics

(i) Find OB→\overrightarrow{OB}OB

(ii) Find OE→\overrightarrow{OE}OE

(iii) Find CD→\overrightarrow{CD}CD

(i) Find AB→\overrightarrow{AB}AB

(ii) Find AC→\overrightarrow{AC}AC

(iii) Find OC→\overrightarrow{OC}OC

(i) Find PQ→\overrightarrow{PQ}PQ​

(ii) Find PX→\overrightarrow{PX}PX

(iii) Find OX→\overrightarrow{OX}OX

(i) Find AB→\overrightarrow{AB}AB

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(i) Find $\overrightarrow{OB}$

(ii) Find $\overrightarrow{OE}$

(iii) Find $\overrightarrow{CD}$

(i) Find $\overrightarrow{AB}$

(ii) Find $\overrightarrow{AC}$

(iii) Find $\overrightarrow{OC}$

(i) Find $\overrightarrow{PQ}$

(ii) Find $\overrightarrow{PX}$

(iii) Find $\overrightarrow{OX}$

(i) Find $\overrightarrow{AB}$