Vector productAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

State the formula for \mathbf a\times\mathbf b in terms of magnitudes.
Components of \mathbf a\times\mathbf b?
How are \mathbf a\times\mathbf b and \mathbf b\times\mathbf a related?
What does \mathbf a\times\mathbf b=\mathbf 0 tell you?
What is \mathbf a\times\mathbf a?
Which two vectors is \mathbf a\times\mathbf b perpendicular to?
What does |\mathbf a\times\mathbf b| represent?
Area of triangle ABC using the vector product?
Vector equation of a line in vector product form?
How do you test whether a point lies on (\mathbf r-\mathbf a)\times\mathbf b=\mathbf 0?
\mathbf i\times\mathbf j, \mathbf j\times\mathbf k, \mathbf k\times\mathbf i?
How do you find the perpendicular distance from C to line AB?
Is the vector product associative?

Exam questions on Vector product

The vectors $\mathbf a=2\mathbf i-\mathbf j+3\mathbf k$ and $\mathbf b=\mathbf i+4\mathbf j-2\mathbf k$ are given.
Show that $\mathbf a\times\mathbf b$ is perpendicular to $\mathbf b$ .2 marks
Triangle $ABC$ has vertices $A(1,0,2)$ , $B(3,2,3)$ and $C(2,-1,5)$ .
Find the exact perpendicular distance from $C$ to the line $AB$ .2 marks
The line $l_1$ has equation $(\mathbf r-\mathbf a)\times\mathbf b=\mathbf 0$ , where $\mathbf a=\begin{pmatrix}1 \\ 2 \\ -1\end{pmatrix}$ and $\mathbf b=\begin{pmatrix}2 \\ -1 \\ 3\end{pmatrix}$ .
Show that the point $(5,0,5)$ lies on $l_1$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).