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A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals
- 45°
- 60°
- 75°
- 30°
Correct answer: 60°
Solution
Direction cosines satisfy l^2+m^2+n^2=1. cos^2(45)=1/2, cos^2(120)=1/4, so cos^2(theta)=1/4 -> cos theta=1/2 -> acute theta=60 deg.
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