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A vector of magnitude sqrt2 coplanar wit...

A vector of magnitude `sqrt2` coplanar with the vectors `veca=hati+hatj+2hatk and vecb = hati + hatj + hatk,` and perpendicular to the vector `vecc = hati + hatj +hatk` is

A

`-hatj+hatk`

B

`hati-hatk`

C

`hati-hatj`

D

`hati-2hatj+hatk`

Text Solution

Verified by Experts

The correct Answer is:
A

A vector coplanar with `hat(i)+hat(j)+2hat(k)` and `hat(i)+2hat(j)+hat(k)` is
`hat(i)+hat(j)+2hat(k)+lambda(hat(i)+2hat(j)+hat(k))=(1+lambda)hat(i)+(1+2 lambda)hat(j)+(2+lambda)hat(k)`
it is perpendicular to `hat(i)+hat(j)+hat(k)`
`:. 1+lambda+1+2 lambda+2+lambda =0" "[ :' a.b=0]`
`implies lambda=-1`
`:.` Required vector is `-hat(j)-hat(k)`.
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