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The component of vec(A)=hat(i)+hat(j)+5h...

The component of `vec(A)=hat(i)+hat(j)+5hat(k)` perpendicular to `vec(B)=3hat(i)+4hat(j)` is

A

`-(4)/(25)hati+(3)/(25)hatj+5hatk`

B

`-(8)/(25)hati-(6)/(25)hatj+5hatk`

C

`(4)/(25)hati-(3)/(25)hatj+5hatk`

D

`+(8)/(25)hati-(6)/(25)hatj+5hatk`

Text Solution

Verified by Experts

The correct Answer is:
C

`vec(A)_(||)=A cos theta=A((vecA.vec(B))/(AB))`
`=(vecA.vec(B))/(B)=(3+4)/(5)=(7)/(5)`
`vec(A)_(||)=(7)/(5)((3hati+4hatj)/(5))=(7)/(25)(3hati+4hatj)`
`vec(A)_(||)=(21)/(25)hati+(28)/(25)hatj`
`vec(A)_(bot)=(hati+hatj+5hatk)=((21)/(25)hati+(28)/(25)hatj)`
`=(4)/(25)hati-(3)/(25)hatj+5hatk`
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