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Question

# If a vector ¯x makes angles with measure π4 and 5π4 with positive directions of X-axis and Y-axis respectively, then ¯x made angle of measure ________ with positive direction of Z-axis.

A
π2
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B
π3
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C
π4
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D
5π3
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Solution

## The correct option is A π2Let α,β and γ be the direction ratios of the vector.and let a,b and c be the direction angles of the vector.Then, Then, α=cos(a)=cosπ4=1√2 β=cos(b)=cos5π4=−1√2γ=cos(c)Now, α2+β2+γ2=1⟹12+12+γ2=1⟹γ=0⟹cos(c)=0⟹c=π2 or c=3π2Hence, the answer is option (A).

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