NECO 2023 · Paper 1 · Q33

Vectors

Find the value of the scalar $\lambda$ for which the vectors $3\mathbf{i} + 5\lambda\mathbf{j}$ and $2\mathbf{i} - 6\mathbf{j}$ are perpendicular.

Worked solution (try it first)

Perpendicular vectors have a scalar product of 0.
The scalar product is $(3)(2) + (5\lambda)(-6) = 6 - 30\lambda$ .
Set $6 - 30\lambda = 0$ : $30\lambda = 6$ , so $\lambda = \frac15$ , option B.

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