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A line AB in three dimensional space makes angles 45° and 120° with the positive x-axis and positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θequals ( in degrees)

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answer is 60.

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Detailed Solution

cos2⁡45∘+cos2⁡120∘+cos2⁡θ=1⇒ cos2⁡θ=1−(1/2)−(−1/2)2=1/4⇒ cos⁡θ=1/2⇒θ=60∘

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A line AB in three dimensional space makes angles 45° and 120° with the positive x-axis and positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θequals ( in degrees)