Given three vectors in three–dimensional space, ,

MATHEMATICS · Subjective · A Level · Mathematics · Vectors · Vectors

Problem

Given three vectors in three–dimensional space,

\mathbf{u}=2\hat{i}-3\hat{j}+\hat{k}

\mathbf{v}=-\hat{i}+4\hat{j}+5\hat{k}

, and

\mathbf{w}=\dfrac{3}{2}\hat{i}-\sqrt{2}\,\hat{j}+4\hat{k}

, answer the following: (a) Calculate the vector

\mathbf{S}=\mathbf{u}+\mathbf{v}-2\mathbf{w}

and express it in

\hat{i},\hat{j},\hat{k}

form. (b) Find the magnitude of

\mathbf{S}

, leaving any surd in simplest form.