Let ( a ) and ( b ) be non-zero

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

Problem

Let

\mathbf{a}

and

\mathbf{b}

be non-zero, non-collinear vectors. Define

\mathbf{u}=3\mathbf{a}-4\mathbf{b}

and

\mathbf{v}=-6\mathbf{a}+8\mathbf{b}.

(a) Show that

\mathbf{u}

and

\mathbf{v}

are parallel. (b) Find the scalar

\lambda

such that

\mathbf{v}=\lambda\mathbf{u}.

|\mathbf{v}|=|\lambda|\,|\mathbf{u}|.

(d) If

|\mathbf{a}|=5,\;|\mathbf{b}|=2

and the angle between

\mathbf{a}

and

\mathbf{b}

60^{\circ},

calculate the magnitudes of

\mathbf{u}

and

\mathbf{v}.