A vector is inclined at equal acute angles to x – axis, y – axis, and z - axis. If units, find

Question

Philoid · Accepted Answer

Here, α = β = γ

⇒ cosα = cosβ = cosγ

⇒ l = m = n = p(say)

Now, we know that -

l² + m² + n² = 1

⇒ p² + p² + p² = 1

⇒ 3p² = 1

∴ the direction cosines of r⃗ are -

⇒ r⃗ = |r⃗|( l î + m ĵ + n k̂)

Now, multiplying and dividing it by √3

⇒ r⃗ = ±2√ 3 ( î + ĵ + k̂)