The scalar productEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

State the component formula for \mathbf{a}\cdot\mathbf{b} in 3D.
State the angle formula for \mathbf{a}\cdot\mathbf{b}.
How do you find \cos\theta between two vectors?
Is a scalar product a vector or a number?
When are non-zero vectors \mathbf{a} and \mathbf{b} perpendicular?
What does \mathbf{a}\cdot\mathbf{a} equal?
What does \mathbf{a}\cdot\mathbf{b}<0 tell you about the angle?
Which vectors give the angle ABC at B?
Evaluate (2\mathbf{i}-\mathbf{j}+3\mathbf{k})\cdot(\mathbf{i}+4\mathbf{j}-\mathbf{k}).
What is |3\mathbf{i}-6\mathbf{j}+2\mathbf{k}|?
How do you find an unknown constant that makes two vectors perpendicular?
Using AB and BC for the angle at B gives what?

Exam questions on The scalar product

The vectors $\mathbf{p}=2\mathbf{i}-3\mathbf{j}+\mathbf{k}$ and $\mathbf{q}=4\mathbf{i}+\mathbf{j}-5\mathbf{k}$ are given.
The vector $\mathbf{r}=\mathbf{i}+2\mathbf{j}+\lambda\mathbf{k}$ is perpendicular to $\mathbf{p}$ . Find the value of $\lambda$ .2 marks
Relative to the origin $O$ , the point $A$ has position vector $2\mathbf{i}+2\mathbf{j}+\mathbf{k}$ and the point $B$ has position vector $3\mathbf{i}-6\mathbf{j}+2\mathbf{k}$ .
Find the size of angle $AOB$ , giving your answer in degrees to 1 decimal place.2 marks
The points $A$ , $B$ and $C$ have coordinates $A(1,-1,2)$ , $B(3,1,3)$ and $C(2,-3,0)$ .
Find the size of angle $BAC$ , giving your answer in degrees to 1 decimal place.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).