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Let L be the line of intersection of t...

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 a.`1/(sqrt(3))` b. `1/2` c. 1 d.`1/(sqrt(2))`

A

`(1)/(2)`

B

1

C

`(1)/(sqrt2)`

D

`(1)/(sqrt3)`

Text Solution

Verified by Experts

The correct Answer is:
d
Since line of intersection is perpendicular to both the planes, direction rations of the line of intersection is ltbgt `|[hati,hatj,hatk],[2,3,1],[1,3,2]|=3hati-3hatj+3hatk`
Hence, `cosalpha=(3)/(sqrt(9+9+9))=(1)/(sqrt3)`
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