Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/vectors/ahl-4-20/problems/b/

jmaths

IB Mathematics: Applications and Interpretation HL · AHL 4: Vectors · AHL 4.20

Mixed practice: scalar and vector products, lines and distances Problem set B Answers

Skills

1. (a) 119°
2. (b) 83.4°
1. (a) 65.4°
2. (b) 134°
3. (c) 2.65
4. (d) \(20 \sqrt{2}\)
5. (e) 0.927 rad
6. (f) 1.12 rad
1. (a) 35.4°
2. (b) 25.2°
3. (c) \(\mathbf{d}_1\cdot\mathbf{d}_2=0\)
4. (d) \(\mathbf{r}=\begin{pmatrix}-1\\4\\3\end{pmatrix}+\lambda \begin{pmatrix}2\\-3\\6\end{pmatrix}\); 31.0°
1. (a) \(6\mathbf{i} - 4\mathbf{j} + 7\mathbf{k}\) (or any multiple of it)
2. (b) \(\dfrac{1}{\sqrt{3}}\begin{pmatrix}1\\-1\\-1\end{pmatrix}\) (or its negative)
3. (c) t = 5.5
4. (d) t = -2 or t = 2.5
1. (a) \(\mathbf{a}\times\mathbf{b}\) is perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\), and the scalar product of perpendicular vectors is 0
2. (b) 0
3. (c) Both sides equal 294
4. (d) \(\mathbf{p}=\begin{pmatrix}3\\-5\\-4\end{pmatrix}\), \(\mathbf{q}=\begin{pmatrix}-3\\5\\4\end{pmatrix}\); \(\mathbf{q}=-\mathbf{p}\)

1. (a) 58.5°, 71.5°, 50.1°
2. (b) 8.96
1. (a) \(\overrightarrow{CA}\cdot\overrightarrow{CB}=0\)
2. (b) A: 36.7°, B: 53.3°
3. (c) 3.35
1. (a) (3, 2, 1)
2. (b) 8.66
1. (a) (3, 3, 4)
2. (b) \(|\overrightarrow{AB}|=|\overrightarrow{AD}|=3\)
3. (c) \(\overrightarrow{AC}\cdot\overrightarrow{BD}=0\)
1. (a) C(1, 7, 1), F(1, 2, 4), G(1, 7, 4), H(-1, 7, 4)
2. (b) 9.50

1. (a) \(\overrightarrow{OB}=\lambda\overrightarrow{OA}\)
2. (b) \(\lambda=2\)
3. (c) \(\sqrt{5}\)
1. (a) M(1, -2, 7)
2. (b) Q is on \(l\) when \(\lambda=-1\)
3. (c) R(5, -10, 15)

jmaths.xyz · AI HL · AHL 4.20 Mixed practice: scalar and vector products, lines and distances