(c) 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 eq. {i} ] ⇒3l2=1 ⇒ l=±
1
√3
Therefore, l = m = n = ±
1
√3
∴ vector r = |r| (±
1
√3
∧
i
±
1
√3
∧
j
±
1
√3
∧
k
) Hence, total number of required vectors = 23 = 8