Statement 1: Unit vectors orthogonal to the vector `3hati+2hatj+6hatk` and coplanar with the vectors `2hati+hatj+hatk` and `hati-hatj+hatk` are `+-1/(sqrt(10))(3hatj-hatk)`.
Statement 2: For any three vectors `veca, vecb,` and `vecc` vector `vecaxx(vecbxxvecc)` is orthogonal to `veca` and lies in the plane of `vecb` and `vecc`.

Options

A. 1
B. 2
C. 3
D. 4

Answer

A

Explanation

Statement -2 is true.
Let `veca=3hati+2hatj+6hatk, vecb=2hati+hatj+hatk` and `vecc=hati-hatj+hatk`
Using statement -2, required unit vectors are given by
`vec(alpha)=+-(vecaxx(vecbxxvecc))/(|vecaxx(vecbxxvecc)|)`
Now `vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc`
`impliesvecaxx(vecbxxvecc)=7(2hati+hatj+hatk)-14(hati-hatj+hatk)=21hatj-7hatk`
`:. vec(alpha)=+-(21hatj-7hatk)/(7sqrt(10))=+-1/(sqrt(10))(3hatj-hatk)`
So, statement -1 is true and statement -2 is a correct explanation of statement 1.