Question

let L be line of intersection of planes 2x+3y+z=1 and x+3y+2z=2.if L makes an angleα
with positive x axis then prove that cos α =1/√3

Answer 1

Given:

Let L be line of intersection of planes 2x+3y+z=1 and x+3y+2z=2.

To find:

If L makes an angleα with positive x axis then prove that cos α =1/√3

Solution:

From given, we have,

The planes 2x + 3y + z = 1 and x + 3y + 2z = 2.

The direction of line L =

i  j  k

2 3 1

1 3 2

solving the above, we get

= 3i - 3j + 3k

Therefore,

cos α = 3/√(3²+3²+3²) = 3/√(9+9+9) = 3/√27 = 3/3√3 = 1/√3

∴ cos α = 1/√3

Hence the required proof.