Mathematics

Mathematics

Problem

Two adjacent sides of a parallelogram ABCDABCD are given by AB⃗=2i^+10j^+11k^\vec{AB} = 2\hat{i} + 10\hat{j} + 11\hat{k} and AD⃗=−i^+2j^+2k^\vec{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 AD′AD' becomes AD′AD' . If AD′AD' makes a right angle with the side ABAB , then the cosine of the angle α\alpha is given by a. 89\frac{8}{9} b. 179\frac{\sqrt{17}}{9} c. 19\frac{1}{9} d. 459\frac{4\sqrt{5}}{9}

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