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Let vec(A)=2hat(i)+hat(j),B=3hat(j)-hat(...

Let `vec(A)=2hat(i)+hat(j),B=3hat(j)-hat(k)` and `vec(C )=6hat(i)-2hat(k)`. Find the value of `vec(A)-2vec(B)+3vec(C )`.

A

`20hat(i)+5hat(j)+4hat(k)`

B

`20hat(i)-5hat(j)-4hat(k)`

C

`4hat(i)+5hat(j)+20hat(k)`

D

`5hat(i)+4hat(j)+10hat(k)`

Text Solution

Verified by Experts

The correct Answer is:
B
`vec(A)-2vec(B)+3vec(C )= (2hat(i)+hat(j))-2(3hat(j)-hat(k))+3(6hat(i)-2hat(k))`
`=2hat(i)+hat(j)-6hat(j)+2hat(k)+18hat(i)-6hat(k)`
`= 20hat(i)-5hat(j)-4hat(k)`
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