Position vectors, displacement vectors and distance Problem set A Answers

1. (a) \(\begin{pmatrix}-4 \\ 9 \\ 5\end{pmatrix}\)
2. (b) \(\begin{pmatrix}4 \\ -9 \\ -5\end{pmatrix}\)

\(3\mathbf{i}-8\mathbf{j}+7\mathbf{k}\)

1. (a) \(2 \sqrt{19}\)
2. (b) \(\sqrt{26}\)

1. (a) \(6\)
2. (b) \(\sqrt{26}\)

\(84.4\) m

\(\begin{pmatrix}6 \\ -2 \\ -1\end{pmatrix}\)

1. (a) \(AB=\sqrt{41},\ AC=\sqrt{41},\ BC=3 \sqrt{10}\)
2. (b) AB = AC, so the triangle is isosceles.

1. (a) \(AB^2=41,\ BC^2=72,\ AC^2=113\)
2. (b) \(41+72=113\)