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A parallelogram has adjacent sides given by the vectors (1)/(√2)î+(1)/(√2)ĵ+k̂ and (1)/(√2)î-(1)/(√2)ĵ+k̂. What is the measure of its acute interior angle?

1. 60°
2. 45°
3. 30°
4. 15°

Correct answer: 60°

Solution

With u=(1/sqrt2,1/sqrt2,1) and v=(1/sqrt2,-1/sqrt2,1), u.v = 1/2-1/2+1 = 1 and |u|=|v|=sqrt2. So cos(angle)=1/2, giving 60 degrees, which is the acute interior angle.

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