OCR MEI C4 — Question 4

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
TopicVectors 3D & Lines

4 You are given that \(\mathbf { a } = 2 \mathbf { i } + 6 \mathbf { j } + 9 \mathbf { k }\) and \(\mathbf { b } = \mathbf { i } + 3 \mathbf { j } - \mathbf { k }\).
  1. Write down a unit vector parallel to a.
  2. Find the value of \(\lambda\) such that \(\mathbf { a } + \lambda \mathbf { b }\) is parallel to \(\mathbf { k }\).
  3. Calculate the size of the angle between \(\mathbf { a }\) and \(\mathbf { b }\).