Q4 of 177 Page 24

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

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)


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