Singapore GCE A-Level · H2 Mathematics

Vectors

30 practice questions, each with the answer and an explanation.

Practise Vectors now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 30 questions

Find the scalar product of $a = 1 i + 2 j + 3 k$ and $b = 4 i - 5 j + 6 k$ .
Find the scalar product of $a = 2 i + 0 j - 1 k$ and $b = 3 i + 4 j + 5 k$ .
Find the scalar product of $a = 1 i + 1 j + 1 k$ and $b = 2 i - 3 j + 4 k$ .
Find the scalar product of $a = 3 i - 2 j + 1 k$ and $b = 1 i + 2 j + 5 k$ .
Find the scalar product of $a = 4 i + 1 j + 0 k$ and $b = - 1 i + 3 j + 2 k$ .
Find the scalar product of $a = 2 i + 2 j - 3 k$ and $b = 1 i + 5 j + 2 k$ .
Find the magnitude of the vector $2 i + 3 j + 6 k$ .
Find the magnitude of the vector $1 i + 2 j + 2 k$ .
Find the magnitude of the vector $4 i + 4 j + 7 k$ .
Find the magnitude of the vector $2 i - 6 j + 9 k$ .
Find the magnitude of the vector $3 i + 4 j + 12 k$ .
Find the magnitude of the vector $6 i + 2 j + 3 k$ .
Find the acute angle between the vectors $122$ and $212$ , correct to 1 decimal place.
Find the acute angle between the vectors $304$ and $122$ , correct to 1 decimal place.
Find the acute angle between the vectors $110$ and $101$ , correct to 1 decimal place.
Find the acute angle between the vectors $2 - 1 2$ and $221$ , correct to 1 decimal place.
Find the vector product $123 \times 456$ .
Find the vector product $210 \times 132$ .
Find the vector product $3 - 1 2 \times 140$ .
Find the vector product $102 \times 031$ .
Find the area of the triangle with vertices $A (0, 0, 0)$ , $B (4, 0, 0)$ and $C (0, 3, 0)$ .
Find the area of the triangle with vertices $A (1, 1, 1)$ , $B (3, 1, 1)$ and $C (1, 4, 1)$ .
Find the area of the triangle with vertices $A (1, 1, 0)$ , $B (1, 1, 5)$ and $C (1, 6, 0)$ .
Find the area of the triangle with vertices $A (2, 2, 2)$ , $B (2, 2, 6)$ and $C (2, 5, 2)$ .
Find the area of the triangle with vertices $A (0, 0, 1)$ , $B (6, 0, 1)$ and $C (0, 8, 1)$ .
Find the area of the triangle with vertices $A (1, 0, 0)$ , $B (1, 0, 3)$ and $C (1, 4, 0)$ .
A line has vector equation $r =$ \begin{pmatrix}1\\2\\3\end{pmatrix} $+ λ$ \begin{pmatrix}1\\1\\1\end{pmatrix}$$. Which point lies on the line?
A line has vector equation $r =$ \begin{pmatrix}2\\0\\1\end{pmatrix} $+ λ$ \begin{pmatrix}2\\1\\0\end{pmatrix}$$. Which point lies on the line?
A line has vector equation $r =$ \begin{pmatrix}0\\1\\4\end{pmatrix} $+ λ$ \begin{pmatrix}1\\0\\2\end{pmatrix}$$. Which point lies on the line?
A line has vector equation $r =$ \begin{pmatrix}3\\3\\3\end{pmatrix} $+ λ$ \begin{pmatrix}1\\2\\2\end{pmatrix}$$. Which point lies on the line?

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