Mathematics 9709 · AS & A Level · Vectors

Vectors — practice question

A plane is described by the equation $4x - y + 5z = 39$. A straight line is parallel to the vector $\mathbf{i} - 3\mathbf{j} + 4\mathbf{k}$ and goes through the point $A(0, 2, -8)$. This line intersects the plane at point $B$.
(a(i))[3]

Determine the coordinates of $B$.

(a(ii))[4]

Determine the acute angle between the line and the plane.

(a(iii))[3]

Point $C$ is on the line and the distance from $C$ to $B$ is twice the distance from $A$ to $B$. Find the coordinates of every possible location of point $C$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Write a general point on the line in vector form and substitute it into the plane equation

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