Question

If vector r with dc's l, m, n is equally inclined to the coordinate axes, then the total number of such vectors is ______.

Options

• 4

• 6

• 8

• 2

Answer 1

If vector r with dc's l, m, n is equally inclined to the coordinate axes, then the total number of such vectors is 8.

Explanation:

We have, vector r with dc's l, m, n is equally inclined to the coordinate axes.

So, l = m = n  ...(i)

As, l² + m² + n² = 1

∴ l² + l² + l² = 1  ...[from equation (i)]

`\implies` 3l² = 1

`\implies` l = `± 1/sqrt(3)`

Therefore, l = m = n = `± 1/sqrt(3)`

∴ vector r = `|r|(± 1/sqrt(3)hati ± 1/sqrt(3)hatj + 1/sqrt(3)hatk)`

Hence, total number of required vectors = 2³ = 8