If , and are linearly dependent vectors and ,…

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

Problem

If a=i^+j^+k^\mathbf{a} = \hat{i} + \hat{j} + \hat{k} , b=4i^+5j^+4k^\mathbf{b} = 4\hat{i} + 5\hat{j} + 4\hat{k} and c=i^+αj^+βk^\mathbf{c} = \hat{i} + \alpha\hat{j} + \beta\hat{k} are linearly dependent vectors and ∣c∣=3|\mathbf{c}| = \sqrt{3} , then (1) α=1,β=−1\alpha = 1, \beta = -1 (2) α=1,β=±1\alpha = 1, \beta = \pm 1 (3) α=−1,β=±1\alpha = -1, \beta = \pm 1 (4) α=±1,β=1\alpha = \pm 1, \beta = 1

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