Practise questions · Salam Academy

SA-FP-VD-G012 marksL1 FoundationNon-calculatorPoint distances

Find the distance from the origin to the plane

2x+y+2z=9

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-Q011 markL1 FoundationNon-calculatorTriple product

If

\mathbf a\cdot(\mathbf b\times\mathbf c)=0

, the three vectors are

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-X021 markL1 FoundationNon-calculatorPoint distances

Find the distance from the origin to the plane

3x+4y=10

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-X031 markL1 FoundationNon-calculatorTriple product

Find the volume of the parallelepiped with edges

\mathbf i

,

2\mathbf j

and

3\mathbf k

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-0012 marksL2 StandardNon-calculatorPoint distances

Find the distance from

(1,1,1)

to the plane

x+2y+2z=14

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-0022 marksL2 StandardNon-calculatorTriple product

Find the volume of the parallelepiped with edges

\begin{pmatrix}1\\0\\0\end{pmatrix}

,

\begin{pmatrix}0\\2\\0\end{pmatrix}

,

\begin{pmatrix}1\\1\\3\end{pmatrix}

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-0042 marksL2 StandardNon-calculatorPoint distances

Find the distance from

(2,3,4)

to the

x

-axis.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-X012 marksL2 StandardNon-calculatorPoint distances

Find the distance from

(1,1,1)

to the plane

2x+y+2z=14

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-X041 markL2 StandardNon-calculatorTriple product

Find the volume of the tetrahedron with vertices

O

,

(1,0,0)

,

(0,2,0)

and

(0,0,3)

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-X052 marksL2 StandardNon-calculatorPoint distances

Find the shortest distance from

(3,4,0)

to the line through the origin in direction

\mathbf i

.

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-0034 marksL3 ExamCalculatorSkew lines

Find the shortest distance between

\mathbf r=s\begin{pmatrix}1\\0\\0\end{pmatrix}

and

\mathbf r=\begin{pmatrix}0\\1\\2\end{pmatrix}+t\begin{pmatrix}0\\1\\1\end{pmatrix}

(to 3 s.f.).

Salam Academy Original Practice · Proposed mark scheme

SA-FP-VD-0053 marksL4 ChallengingNon-calculatorTriple product

The vectors

\begin{pmatrix}1\\2\\k\end{pmatrix}

,

\begin{pmatrix}0\\1\\1\end{pmatrix}

,

\begin{pmatrix}1\\0\\1\end{pmatrix}

are coplanar. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

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