Question

Let L be the line of intersection of the planes `2x""+""3y""+""z""=""1` and `x""+""3y""+""2z""=""2` . If L makes an angles ` alpha `with the positive x-axis, then cos` alpha ` equals `1/(sqrt(3))` `1/2` 1 `1/(sqrt(2))`
A. `1`
B. `1/(sqrt(2))`
C. `1/(sqrt(3))`
D. `1/2`

Answer 1

Correct Answer - C
Vectors normals to the given planes are `vecn_(1)=2hati+3hatj+k` and `vecn_(2)=hati+3hatj+2hatk`. So the line `L` is parallel
`vecn_(1)=vecn_(1)xxvecn_(2)=|(hati,hatj,hatk),(2,3,1),(1,3,2)|=3hati-3hatj+3hatk`
`implies cos alpha=(vecn.hati)/(|vecn||hati|)=3/(3sqrt(3))=1/(sqrt(3))`