Vectors in three dimensionsAQA A-Level Maths: Flashcards

What these 12 flashcards ask

What does the unit vector \mathbf k represent?
Magnitude of x\mathbf i+y\mathbf j+z\mathbf k?
Magnitude of 2\mathbf i-3\mathbf j+6\mathbf k?
Distance between points with position vectors \mathbf a and \mathbf b?
How do you find \overrightarrow{AB}?
How do you test that two 3D vectors are parallel?
How do you find a unit vector in the direction of a?
Position at time t with constant velocity \mathbf v?
What is speed in vector terms?
When do two moving bodies collide?
Why check the third component of a collision?
Vector forms for constant acceleration?

Exam questions on Vectors in three dimensions

The vectors $\mathbf a=2\mathbf i-3\mathbf j+6\mathbf k$ and $\mathbf b=\mathbf i+2\mathbf j-2\mathbf k$ .
Find the exact distance between the points with position vectors $\mathbf a$ and $\mathbf b$ .2 marks
The points $A$ and $B$ have position vectors $\mathbf a=\mathbf i+2\mathbf j+3\mathbf k$ and $\mathbf b=4\mathbf i-2\mathbf j+15\mathbf k$ relative to the origin $O$ .
The point $C$ is such that $\overrightarrow{AC}=2\overrightarrow{AB}$ . Find the position vector of $C$ .2 marks
$\mathbf u=2\mathbf i-\mathbf j+4\mathbf k$ , $\mathbf v=-6\mathbf i+3\mathbf j+\mu\mathbf k$ and $\mathbf w=2\mathbf i+3\mathbf j+q\mathbf k$ , where $\mu$ and $q$ are constants.
Given that $\mathbf u$ and $\mathbf v$ are parallel, find the value of $\mu$ .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).