2023 RI Promo Q3
2023 RI Promo Q3
8 marks
Promo
Vectors \(\mathbf{a}\) and \(\mathbf{b}\) are such that the magnitude of \(\mathbf{a}\) is \(2\) and \(\mathbf{b}\) is a unit vector perpendicular to \(\mathbf{a}\).
- Find the area of the parallelogram with adjacent sides formed by the vectors \(\mathbf{a}+3\mathbf{b}\) and \(5\mathbf{a}-4\mathbf{b}\).[3]
A vector \(\mathbf{c}\) is such that \(\mathbf{b}\times \mathbf{c}=21\left( \mathbf{a}\times \mathbf{b} \right)\).
- Show that \(\mathbf{c}=\lambda \mathbf{b}-21\mathbf{a}\), where \(\lambda \) is a constant.[2]
- Give the geometrical meaning of \(\left| \mathbf{b}\cdot \mathbf{c} \right|\) and find the possible values of \(\lambda \) if \(\left| \mathbf{b}\cdot \mathbf{c} \right|=5\).[3]
Video Solution:
Video solution locked
A free account saves your progress; this video needs tuition enrolment.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a) \({38}\) (c) \({\left| \mathbf{b} \cdot \mathbf{c} \right| = \left| \mathbf{c} \cdot \mathbf{b} \right|}\) is the length of the projection of \({\mathbf{c}}\) onto \({\mathbf{b}}\). \({\left| \mathbf{b} \cdot \mathbf{c} \right| = \left| \lambda \right|}\). Since \({\left| \mathbf{b} \cdot \mathbf{c} \right| = 5}\), \({\lambda = \pm 5}\).
Need help? Join our JC Math tuition classes.
Learn more