Mathematics 9709 · AS & A Level · Vectors

Vectors — practice question

The line $l$ is defined by ${\bf r} = {\bf i} + 2{\bf j} - {\bf k} + \lambda(3{\bf i} - 2{\bf j} + 2{\bf k})$ and the plane $p$ is given by $2x + 3y - 5z = 18$.
(a(i))[3]

Determine the position vector of the point where $l$ and $p$ meet.

(a(ii))[4]

Determine the acute angle between $l$ and $p$.

(a(iii))[5]

A second plane $q$ is perpendicular to plane $p$ and contains line $l$. Find the equation of $q$, writing your answer in the form $ax + by + cz = d$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write a general point on line $l$ in component form, for example $(1+3\lambda,2-2\lambda,-1+2\lambda)$” …

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