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If vec(P)=hat(i)+hat(j)-hat(k) and vec(Q...

If `vec(P)=hat(i)+hat(j)-hat(k)` and `vec(Q)=hat(i)-hat(j)+hat(k)`, then unit vector along `(vec(P)-vec(Q))` is `:`

A

`(1)/(sqrt(2))hat(i)-(1)/(2)hat(k)`

B

`(sqrt(2)hat(j)-sqrt(2)hat(k))/(2)`

C

`(hat(j)-hat(k))/(2sqrt(2))`

D

`(2hat(j)-2hat(k))/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
`vec(P)-vec(Q)=(hat(i)+hat(j)-hat(k))-(hat(i)-hat(j)+hat(k))=2hat(j)-2hat(k)`
`:. ` unit vector along
`vec(P)-vec(Q)=((vec(P)-vec(Q)))/(|vec(P)-vec(Q)|)=(2hat(j)-2hat(k))/(sqrt((2)^(2)+(-2)^(2)))`
`:. vec(P)-vec(Q)=((vec(P)-vec(Q)))/(|vec(P)-vec(Q)|)=(2hat(j)-2hat(k))/(sqrt((2)^(2)+(-2)^(2)))`
`=(2hat(j)-2hat(k))/(sqrt(4+4))=(2hat(j)-2hat(k))/(2sqrt(2))=(hat(j)-hat(k))/(sqrt(2))`
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