Question

If the direction cosines of a line are `< 1/c, 1/c, 1/c >` then ______.

Options

• c > 0

• 0 < c < 1

• c = `±sqrt3`

• 𝑐 > 2

Answer 1

If the direction cosines of a line are `< 1/c, 1/c, 1/c >` then `underlinebb(c = ±sqrt3)`.

Explanation:

Direction cosines of a line are `< 1/c, 1/c, 1/c >`, then they must satisfy the basic property of direction cosines:

l² + m² + n² = 1

Here l = m = n = `1/c`

`(1/c)^2 + (1/c)^2 + (1/c)^2 = 1`

`3/c^2 = 1`

c² = 3

c = `±sqrt3`