Moderate -0.8 This is a 1-mark vector product question requiring recognition that a×a=0, making the first and fourth expressions simplify to a×b and -a×b respectively, while the middle expressions give a×b and -a×b. It's straightforward pattern recognition with basic vector product properties, easier than average but not trivial since it requires knowing the cross product property rather than just algebraic manipulation.
Three of the four expressions below are equivalent to each other.
Which of the four expressions is not equivalent to any of the others?
Circle your answer.
[1 mark]
\(\mathbf{a} \times (\mathbf{a} + \mathbf{b})\) \quad \((\mathbf{a} + \mathbf{b}) \times \mathbf{b}\) \quad \((\mathbf{a} - \mathbf{b}) \times \mathbf{b}\) \quad \(\mathbf{a} \times (\mathbf{a} - \mathbf{b})\)
Three of the four expressions below are equivalent to each other.
Which of the four expressions is not equivalent to any of the others?
Circle your answer.
[1 mark]
$\mathbf{a} \times (\mathbf{a} + \mathbf{b})$ \quad $(\mathbf{a} + \mathbf{b}) \times \mathbf{b}$ \quad $(\mathbf{a} - \mathbf{b}) \times \mathbf{b}$ \quad $\mathbf{a} \times (\mathbf{a} - \mathbf{b})$
\hfill \mbox{\textit{AQA Further Paper 2 2020 Q1 [1]}}