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

• `sqrt(3)/2`

• `sqrt(2)/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 `2/7`.

Explanation:

Direction ratios of the normal to the plane 2x – 3y + 6z – 11 = 0 are 2, – 3, 6 

Direction ratios of x-axis are 1, 0, 0

∴ Angle between plane and line is

`sin theta = (2(1) - 3(0) + 6(0))/(sqrt((2)^2 + (-3)^2 + (6^2))*sqrt((1)^2 + (0)^2 + (0)^2)`

= `2/sqrt(4 + 9 + 36)`

= `2/7`