3.13 Scalar and vector productsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 3.13 Scalar and vector products

1. 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
2. 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
3. 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