Question

The plane 2x - 3y + 6z - 11 = 0 makes an angle sin^-1 (α) with X-axis. The value of α is equal to ______ 

Options

• `sqrt3/2`

• `sqrt2/3`

• `2/7`

• `3/7`

Answer 1

The plane 2x - 3y + 6z - 11 = 0 makes an angle sin^-1 (α) with X-axis. The value of α is equal to `underline(2/7)`.

Explanation:

d.r.s. of normal to the plane are 2, -3, 6

d.r.s. of X-axis are 1, 0, 0.

∴ The angle between the plane and X-axis is

sin θ = `|(2(1) - 3(0) + 6(0))/(sqrt(4 + 9 + 36).sqrt1)|`

= `2/7`

∴ θ = `sin^-1(2/7)`

But θ = `sin^-1alpha`

∴ `alpha = 2/7`