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))`

Options

A. `1//sqrt(3)`
B. `1//2`
C. 1
D. `1//sqrt(2)`

Answer

A

Explanation

Let the direction cosines of line L be l,m,n. Since , the line intersect the given planes, then the normal to the planes are perpendicular to the line L.
`:." "2l+3m+n=0` . . . (i)
` and" "1+3m+2n=0` . . . (ii)
From Eqs. (i) and (ii), we get
`(l)/(3)=(m)/(-3)=(n)/(3)=k" "` [say]
We know that `l^(2)+m^(2)+n^(2)=1`
`:." "(3k)^(2)+(-3k)^(2)+(3k)^(2)=1`
`rArr" "27k^(2)=1`
`rArr" "K=(1)/(3sqrt(3))`
`:." "l=(1)/(sqrt(3))rArr cos alpha=(1)/(sqrt(3))`