Question

If a line makes angles of `(3pi)/4, pi/3` and θ with the positive directions of x, y and z-axis respectively, then θ is ______.

विकल्प

• `(-pi)/3  only`

• `pi/3  only`

• `pi/6` 

• `± pi/3`

Answer 1

If a line makes angles of `(3pi)/4, pi/3` and θ with the positive directions of x, y and z-axis respectively, then θ is `bbunderline(pi/3  only)`.

Explanation:

According to the question,

`l = cos  (3pi)/4 = (-1)/sqrt2`

m = `cos  pi/3 = 1/2`

n = cos θ

l² + m² + n² = 1

`((-1)/sqrt2)^2 + (1/2)^2 + cos^2 θ = 1`

`1/2 + 1/4 + n^2 = 1`

`(2 + 1)/4 + n^2 = 1`

`3/4 + n^2 = 1`

`n^2 = 1 - 3/4`

`n^2 = (4 - 3)/4`

= `1/4`

∴ `n = 1/2    ...[∵ n ≠ (-1)/2 "positive direction"]`

∴ `cos θ = 1/2`

∴ θ = `pi/3`