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AB = 2i + 10j + 11k, AD = -i + 2j + 2k: AD rotated in the plane until it is perpendicular to AB, find cos alpha

The same question, asked 4 times: 12 May 2024 S1, 12 May 2024 S2, 17 Apr 2026 S1, 19 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    12 May 2024 S1

    103
    Two adjacent sides of a parallelogram ABCD are given by AB→=2i^+10j^+11k^\overrightarrow{AB}=2\hat{i}+10\hat{j}+11\hat{k} and AD→=−i^+2j^+2k^\overrightarrow{AD}=-\hat{i}+2\hat{j}+2\hat{k}. The side AD is rotated by an acute angle α\alpha in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with side AB, then the cosine of the angle α\alpha is given by

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  2. Question 2

    12 May 2024 S2

    141
    Two adjacent sides of parallelogram ABCD are given by AB→=2i^+10j^+11k^\overrightarrow{AB} = 2\hat{i}+10\hat{j}+11\hat{k} and AD→=−i^+2j^+2k^\overrightarrow{AD} = -\hat{i}+2\hat{j}+2\hat{k}. The side AD is rotated by angle α\alpha in plane of parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle α\alpha is given by

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  3. Question 3

    17 Apr 2026 S1

    92
    Two adjacent sides of a parallelogram ABCD are given by AB‾=2i^+10j^+11k^\overline{AB} = 2\hat{i} + 10\hat{j} + 11\hat{k} and AD‾=−i^+2j^+2k^\overline{AD} = -\hat{i} + 2\hat{j} + 2\hat{k}. The side AD is rotated by an acute angle α\alpha in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle α\alpha is given by

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  4. Question 4

    19 Apr 2026 S2

    88
    Two adjacent sides of a parallelogram ABCD are given by AB‾=2i^+10j^+11k^\overline{AB} = 2\hat{i} + 10\hat{j} + 11\hat{k} and AD‾=−i^+2j^+2k^\overline{AD} = -\hat{i} + 2\hat{j} + 2\hat{k}. The side ADAD is rotated by an acute angle α\alpha in the plane of the parallelogram so that ADAD becomes AD′AD'. If AD′AD' makes a right angle with the side ABAB, then the cosine of the angle α\alpha is...

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