Vectors in three dimensionsEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

What does \mathbf{k} represent?
Write the position vector of (x,y,z).
Give the magnitude of x\mathbf{i}+y\mathbf{j}+z\mathbf{k}.
State the 3D distance formula.
How do you find \overrightarrow{AB} in 3D?
What is the position vector of the midpoint of AB?
Find the length of the diagonal of a cuboid a by b by c.
How do you add two 3D vectors?
What is the magnitude of 3\mathbf{i}+4\mathbf{j}+12\mathbf{k}?
How do you test for a right angle at A in triangle ABC?
What does a negative \mathbf{k} component mean in a context with \mathbf{k} upwards?
If \overrightarrow{AC}=2\overrightarrow{AB}, how do you get \overrightarrow{OC}?

Exam questions on Vectors in three dimensions

Relative to an origin $O$ , the points $A$ and $B$ have coordinates $(2,-1,3)$ and $(5,3,15)$ .
The point $C$ is such that $\overrightarrow{AC}=2\overrightarrow{AB}$ . Find the position vector of $C$ .2 marks
A drone flies from a point $P$ to a point $Q$ . Relative to an origin $O$ at ground level, with $\mathbf{i}$ pointing east, $\mathbf{j}$ north and $\mathbf{k}$ vertically upwards (distances in metres), $P$ has position vector $4\mathbf{i}-2\mathbf{j}+7\mathbf{k}$ and $Q$ has position vector $-2\mathbf{i}+4\mathbf{j}+4\mathbf{k}$ .
Find the exact distance $PQ$ .2 marks
Relative to an origin $O$ , the points $A$ , $B$ and $C$ have position vectors $\mathbf{a}=\mathbf{i}-\mathbf{j}+2\mathbf{k}$ , $\mathbf{b}=3\mathbf{i}+\mathbf{j}+3\mathbf{k}$ and $\mathbf{c}=-\mathbf{i}+4\mathbf{k}$ .
Show that $AB=AC$ .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).