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The projection of the vector vecA = hat ...

The projection of the vector `vecA = hat - 2hatj + hatk` on the vector `vecB = 4hati - 4hatj + 7hatk` is

A

`(19)/(9)`

B

`(38)/(9)`

C

`(8)/(9)`

D

`(4)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
A
Here, `vec(A)=hati-2hatj+hatk,vec(B)=4hati-4hatj+7hatk`
The propection of `vec(A)" on "vec(B)=Acostheta`
`Acostheta=(ABcostheta)/(B)=(vec(A).vec(B))/(B)=((hati-2hatj+hatk).(4hati-4hatj+7hatk))/(sqrt((4)^(2)+(-4)^(2)+(7)^(2)))`
`=(19)/(9)`
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