If a vector r=xi^+yj^+zk^, makes angle π3,π3 and πn with X-axis, Y-axis and Z-axis respectively. The value of n is _______.

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answer is 4.

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Detailed Solution

cos2⁡α+cos2⁡β+cos2⁡γ=1 or cos2⁡60∘+cos2⁡60∘+cos2⁡γ=1 or 14+14+cos2⁡γ=1 or cos2⁡γ=1−12=12 or cos⁡γ=12⇒γ=π4 ∴ n=4

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