Dot Product of Vectors

What type of quantity is produced by the dot product of two vectors?

• scalar
• vector

If the dot product of two vectors is equal to zero, then what do we know about the two vectors?

• They are parallel.

• They are orthogonal.

• They are neither.

How do you know if two vectors are orthogonal?

• Their sum is 0.
• The dot product is 1.
• The angle between them is 0°.
• The dot product is 0.

Tags

CCSS.HSG.GPE.B.5

CCSS.HSN.VM.A.1

CCSS.HSG.CO.A.1

Given parallel vectors u and v. Answer ALL that apply

• their scalar product is zero

• their scalar product is either 1 or -1

• u is a scalar multiple of v

• magnitude of u equals the magnitude of v

Tags

CCSS.HSG.GPE.B.5

CCSS.HSN.VM.A.1

CCSS.HSG.CO.C.9

CCSS.HSN.VM.C.11

If ||v||= 8, ||w||=6 and the angle between them is θ = 240˚ $Find\ \overrightarrow{\ \ v}.\overrightarrow{\ \ w}$  

• -24

• 24

• 48

• -48

What operation you need to find an angle between two vectors?

• Dot product between the two vectors

• Dot product between the two vectors divide the magnitude of both vectors

• Cosine inverse of dot product between the two vectors divide the magnitude of both vectors

• Cross product between the two vectors

What is the angle between two orthogonal vectors?

• 180 degree

• 90 degree

• 60 degree

• 45 degree

If $\overrightarrow{\ \ a}=3i\ +5j+k\ \ and\ \overrightarrow{\ \ b}=2i+j+3k\ then\ \overrightarrow{\ \ a}\ .\overrightarrow{\ \ b}=$  

• 41

• 12

• 21

• 14

Projection of $\overrightarrow{\ \ a\ }\ =2i-3j-5k\ on\ \overrightarrow{\ \ b}=i-j-k\ is$  

• 10

•  $10\sqrt{3}$  

•  $\frac{10\sqrt{3}}{3}$  

• --10

If $\overrightarrow{\ \ a\ }=5i-7j-2k\ is\ perpendicular\ to\ \overrightarrow{\ \ b}\ =2i\ +pj+3k\ then\ p\ =$  

• 6/4

• 7/4

• 4/6

• 4/7