Consider and

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

Problem

Consider a=⟨2, ⁣−1, 2⟩\mathbf a = \langle 2,\!-1,\,2\rangle and b=⟨k, ⁣−k2, k⟩\mathbf b = \langle k,\!-\tfrac{k}{2},\,k\rangle. The two vectors are always parallel. For which value of kk do they have the same magnitude and point in opposite directions? (a) k=−4k=-4 (b) k=−2k=-2 (c) k=2k=2 (d) k=−655k=-\dfrac{6\sqrt5}{5}

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