If ABCD is parallelogram

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

If ABCD is parallelogram, AB=2i^+4j^−5k^\mathbf{AB} = 2\hat{i} + 4\hat{j} - 5\hat{k} and AD=i^+2j^+3k^\mathbf{AD} = \hat{i} + 2\hat{j} + 3\hat{k} , then the unit vectors in the direction of BD\mathbf{BD} is (1) 169(i^+2j^−8k^)\frac{1}{\sqrt{69}}(\hat{i} + 2\hat{j} - 8\hat{k}) (2) 169(i^+2j^−8k^)\frac{1}{69}(\hat{i} + 2\hat{j} - 8\hat{k}) (3) 169(−i^−2j^+8k^)\frac{1}{\sqrt{69}}(-\hat{i} - 2\hat{j} + 8\hat{k}) (4) 169(−i^−2j^+8k^)\frac{1}{69}(-\hat{i} - 2\hat{j} + 8\hat{k})

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