An incident ray is given by the vector (in arbitrary units)

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

Problem

An incident ray is given by the vector

\mathbf{s}=4\,\hat{\mathbf{i}}+3\,\hat{\mathbf{j}}-12\,\hat{\mathbf{k}}

(in arbitrary units). The reflecting plane has a unit normal

\hat{\mathbf{n}}=\tfrac{1}{\sqrt{3}}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})

. Determine the vector of the reflected ray.