Mathematics

Problem

Let

\vec{a}=3\mathbf{i}-4\mathbf{j}+2\mathbf{k}

and

\vec{b}=-\mathbf{i}+5\mathbf{j}+4\mathbf{k}

. Define the vector

\vec{r}=2\vec{a}-\vec{b}

. (a) Express

\vec{r}

in component form. (b) Calculate

|\vec{r}|

. (c) If

\lambda

is a real number such that

|\,\vec{r}-\lambda\vec{b}\,|=|\vec{b}|

, determine the value(s) of

\lambda