Q. 45.0( 1 Vote )

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

Answer :

Here, α = β = γ

⇒ cosα = cosβ = cosγ

⇒ l = m = n = p(say)

Now, we know that -

l^{2} + m^{2} + n^{2} = 1

⇒ p^{2} + p^{2} + p^{2} = 1

⇒ 3p^{2} = 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)

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