Let , and . If the vectors, , and are coplanar, then is equal…

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

Problem

Let

\mathbf{a} = \hat{i} + \hat{j}

\mathbf{b} = \hat{j} + \hat{k}

and

\mathbf{c} = \alpha\mathbf{a} + \beta\mathbf{b}

. If the vectors,

\hat{i} - 2\hat{j} + \hat{k}

3\hat{i} + 2\hat{j} - \hat{k}

and

\mathbf{c}

are coplanar, then

\frac{\alpha}{\beta}

is equal to (1) 1 (2) 2 (3) 3 (4) -3