Hint
Choose a consistent coordinate orientation. Form a₂b₃−a₃b₂.
Worked solution
(a)
\(c=\left[\begin{matrix}9\\-72\\8\end{matrix}\right]\)
Answer: \(9\).
Answer: \(9\)
(b)
\(c=\left[\begin{matrix}9\\-72\\8\end{matrix}\right]\)
Answer: \(-72\).
Answer: \(-72\)
(c)
\(|c|=73\)
Answer: \(73\).
Answer: \(73\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit valid alternative reasoning and consequential working; do not award a reasoning mark for an unexplained final answer.
(a) · 2 marks
- 1 mark: Form a₂b₃−a₃b₂.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Reversing the product reverses its sign.
(b) · 2 marks
- 1 mark: Use the alternating sign in the middle component.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: A cross product is a vector, whereas a scalar triple product is a number.
(c) · 2 marks
- 1 mark: Take the Euclidean norm of the cross product.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Reversing the product reverses its sign.
Total: 6 marks.