Mathematics 9709 · AS & A Level · Vectors

Vectors — practice question

The vector equations of the lines $l$ and $m$ are given by $l: \ \mathbf{r} = 2\mathbf{i} + \mathbf{j} - 3\mathbf{k} + \lambda(-\mathbf{i} + 2\mathbf{k})$ and $m: \ \mathbf{r} = 2\mathbf{i} + \mathbf{j} - 3\mathbf{k} + \mu(2\mathbf{i} - \mathbf{j} + 5\mathbf{k})$. The two lines $l$ and $m$ meet at the point $P$.
(a)[1]

State the coordinates for $P$.

(b)[3]

Find the exact value of the cosine of the acute angle formed by $l$ and $m$.

(c)[3]

Point $A$ on line $l$ has coordinates $(0, 1, 1)$, while point $B$ on line $m$ has coordinates $(0, 2, -8)$. Determine the exact area of triangle $APB$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the point as $P(2,1,-3)$.” …

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI