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If vec(A)=2hat(i)+hat(j)+hat(k) and vec...

If `vec(A)=2hat(i)+hat(j)+hat(k)` and `vec(B)=hat(i)+2hat(j)+2hat(k)`, find the magnitude of compinent of `(vec(A)+vec(B))` along `vec(B)`

A

`4` unit

B

`5` unit

C

`6` unit

D

`7` unit

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Verified by Experts

The correct Answer is:
B
`vec(A)+vec(B)=3hat(i)+3hat(j)+3hat(k)=3(hat(i)+hat(j)+hat(k))`
component of `(vec(A)+vec(B))` along `vec(B)=((vec(A)+vec(B)).vec(B))/(B)`
`=3xx((1+2+2))/(3)=5`
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