The vector (s) which is (are) coplanar with vectors `hati+hatj+2hatk` and `hati+2hatj+hatk`, and perpendicular to the vector `hati+hatj+hatk`, is/are

Options

A. `hatj-hatk` and `-hatj+hatk`
B. `-hati+hatj` and `hati-hatj`
C. `hati-hatj` and `hatj-hatk`
D. `-hatj+hatk` and `-hati+hatj`

Answer

Minimum value at `(alpha)^(alpha)^(x)` + alpha^(1-(alpha)^x)` is

Explanation

Required vector are parallel to the vector `vecr` given by
`vecr=veaxx(vecbxxvecc)` where `veca=hati+hatj+hatk, vecb=hati+hatj+2hatk`
and `vecc=hati+2hatj+hatk`
`implies vecr=(veca.vecc)vecb-(vecc.vecb)vecc`
`impliesvecr=4(hati+hatj+2hatk)-4(hati+2hatj+hatk)=4(-hatj+hatk)`
Hence, required vectors are parallel to the vector `=4(-hatj+hatk)`