If vector r → with direction cosine l , m , n is equally inclined to the co-ordinate axes, then the total number of such vectors is

Question

If vector r → with direction cosine l , m , n is equally inclined to the co-ordinate axes, then the total number of such vectors is, 4, 6, 8, 2

MARKS App · Accepted Answer

r ¯ = r ¯ ± 1 3 i ^ ± 1 3 j ^ ± 1 3 k ^ For equally inclined to co-ordinate axes. ⇒ | l | = | m | = | n | ⇒ l 2 + m 2 + n 2 = 1 ⇒ 3 l 2 = 1 ⇒ l 2 = 1 3 ⇒ l = ± 1 √ 3 = m = n ⇒ l , m , n each has 2 choices. ∴ Total lines = 2 3

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