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 " "l+3m+2n=0` . . .(ii)
From Eqs. (i) and (ii), we get
`(l)/(3)=(m)/(-3)=(n)/(3)=k" "` [say]
We known that, `l^(2)+m^(2)+n^(2)=1`
`:." "(3k)^(2)+(-3k)^(2)+(3k)^(2)=1`
`rArr" "k=(1)/(3sqrt(3))`
`:." "l=(1)/(sqrt(3))rArrcosalpha=(1)/(sqrt(3))`