If is perpendicular to and is non-zero scalar such that

MATHEMATICS · Single correct · A Level · Mathematics · Vectors · Vectors

Problem

\mathbf{a}

is perpendicular to

\mathbf{b}

and

p

is non-zero scalar such that

p\mathbf{r} + (\mathbf{r} \cdot \mathbf{b})\mathbf{a} = \mathbf{c}

, then

\mathbf{r}

(1)

[\mathbf{r} \mathbf{a} \mathbf{c}] = 0

(2)

p^2\mathbf{r} = p\mathbf{a} - (\mathbf{c} \cdot \mathbf{a})\mathbf{b}

(3)

p^2\mathbf{r} = p\mathbf{b} - (\mathbf{a} \cdot \mathbf{b})\mathbf{c}

(4)

p^2\mathbf{r} = p\mathbf{c} - (\mathbf{b} \cdot \mathbf{c})\mathbf{a}