The plane passing through the origin contains the vectors and

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

Problem

The plane passing through the origin contains the vectors u=2i+k\mathbf{u}=2\mathbf{i}+\mathbf{k} and v=i−3j\mathbf{v}=\mathbf{i}-3\mathbf{j}. Which of the following is a unit vector normal to this plane whose yy-component is negative? (a) 146 (3i+j−6k)\dfrac{1}{\sqrt{46}}\,( 3\mathbf{i}+\mathbf{j}-6\mathbf{k} ) (b) 146 (−3i−j+6k)\dfrac{1}{\sqrt{46}}\,( -3\mathbf{i}-\mathbf{j}+6\mathbf{k} ) (c) 146 (−3i−j+6k)\dfrac{1}{46}\,( -3\mathbf{i}-\mathbf{j}+6\mathbf{k} ) (d) 110 (−3i−j+6k)\dfrac{1}{\sqrt{10}}\,( -3\mathbf{i}-\mathbf{j}+6\mathbf{k} )

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