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The vectors which is/are coplanar with v...

The vectors which is/are coplanar with vectors `hati+hatj+2hatk and hati+2hatj+hatk` and perpendicular to the vector `hati+hatj+hatk ` is /are (A) `hatj-hatk` (B) `-hati+hatj` (C) `hati-hatj` (D) `-hatj+hatk`

A

`hatj - hatk`

B

`-hati + hatj`

C

`hati -hatj`

D

`-hatj +hatk`

Text Solution

Verified by Experts

The correct Answer is:
a,d
Any vector in the plane of `veca = hati +hatj + 2hatk and vecb = hati + 2hatj + hatk` is
`vecr=lamda(hati+hatj+2hatk) +mu(hati+2hatj+hatk)`
`= (lamda+mu)hati+(lamda+2mu)hatj= (2lamda+mu)hatk`
Also `vecr` is perpendicular to the vector `hati + hatj +hatk`
`Rightarrow vecr.vecc=0`
` Rightarrow lamda + mu =0`
Possible vectors are `hatj -hatk or -hatj +hatk`
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