A vector is inclined at equal angles to the three axes. If the magnitude of is find

Let l, m, n be the direction cosines of the vector r⃗

Vector r⃗ is inclined at equal angles to the three axes.

l = cosα, m = cos α, n = cosα

⇒ l = m = n.

Also, we know that -

l² + m² + n² = 1

cos²α + cos²α + cos²α = 1

3 cos²α = 1

Hence, the direction cosines of the vector which are equally inclined to the axes are

∴ r⃗ = |r⃗ |( l î + m ĵ + n k̂)

(Given, |r⃗ | = 2√ 3 )

⇒ r⃗ = ±(2 î + 2ĵ + 2 k̂)