3.13 Scalar and vector productsIB Maths: Applications and Interpretation HL: Flashcards

What these 14 flashcards ask

How do you calculate \mathbf{v}\cdot\mathbf{w} from components?
Geometric form of the scalar product?
Test for perpendicular vectors?
Formula for the angle between two vectors?
What does a negative scalar product tell you about the angle?
How do you find the acute angle between two lines?
Component of \mathbf{a} in the direction of \mathbf{b}?
Component of \mathbf{a} perpendicular to \mathbf{b}?
Definition of the vector product?
Is the result of \mathbf{v}\times\mathbf{w} a number or a vector?
How are \mathbf{v}\times\mathbf{w} and \mathbf{w}\times\mathbf{v} related?
Area of the parallelogram with sides \mathbf{v} and \mathbf{w}?
Area of the triangle with sides \mathbf{v} and \mathbf{w}?
Distance from C to line AB using the vector product?

Exam questions on 3.13 Scalar and vector products

Two forces $\mathbf{a}=\begin{pmatrix} 3 \\ 1 \\ 2 \end{pmatrix}$ N and $\mathbf{b}=\begin{pmatrix} 1 \\ -2 \\ 4 \end{pmatrix}$ N act on a particle.
A third force $\mathbf{c}=\begin{pmatrix} k \\ -1 \\ 2 \end{pmatrix}$ N is perpendicular to $\mathbf{a}$ . Find the value of $k$ .2 marks
A triangular roof panel has corners $A(1,0,2)$ , $B(4,2,1)$ and $C(2,3,5)$ , where the coordinates are in metres.
Find the shortest distance from $C$ to the line through $A$ and $B$ .2 marks
Two straight pipes are modelled by the lines $l_1:\ \mathbf{r}=\begin{pmatrix} 1 \\ 0 \\ 2 \end{pmatrix}+s\begin{pmatrix} 2 \\ 1 \\ -2 \end{pmatrix}$ and $l_2:\ \mathbf{r}=\begin{pmatrix} 3 \\ -1 \\ 0 \end{pmatrix}+t\begin{pmatrix} 1 \\ -2 \\ 2 \end{pmatrix}$ , where the units are metres.
Use your GDC to find the acute angle between the two pipes.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).