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Let L be the line of intersection of ...

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`

Text Solution

Verified by Experts

The correct Answer is:
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))`
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