Express the vector as sum of two vectors such that one is parallel to the vector and…

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Express the vector

\mathbf{a} = 5\hat{i} - 2\hat{j} + 5\hat{k}

as sum of two vectors such that one is parallel to the vector

\mathbf{b} = 3\hat{i} + \hat{k}

and the other is perpendicular to

\mathbf{b}