Mathematics 9709 · AS & A Level · Vectors

Vectors — practice question

Plane $m$ is given by $x + 4y - 8z = 2$. Plane $n$ is parallel to $m$ and goes through $P$, whose coordinates are $(5, 2, -2)$.
(i)[2]

Find the equation of $n$, and give your answer in the form $ax + by + cz = d$.

(ii)[3]

Calculate the perpendicular distance between $m$ and $n$.

(iii)[4]

The line $l$ is in plane $n$, passes through $P$ and is perpendicular to $OP$, where $O$ is the origin. Find a vector equation for $l$.

(c(iii))[4]

The line $l$ lies in plane $p$, passes through $P$ and is perpendicular to $OP$, where $O$ is the origin. Find a vector equation for $l$.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: Put coordinates $(5,2,-2)$ into $x+4y-8z=d$

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