OCR MEI Further Pure Core 2024 June — Question 5

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2024
SessionJune
TopicVectors: Cross Product & Distances

5
  1. Given that \(\mathbf { u } = \left( \begin{array} { r } - 2
    1
    2 \end{array} \right) , \mathbf { v } = \left( \begin{array} { l } a
    0
    1 \end{array} \right)\) and \(\mathbf { u } \times \mathbf { v } = \left( \begin{array} { l } 1
    b
    3 \end{array} \right)\), find \(a\) and \(b\).
  2. Using \(\mathbf { u } \times \mathbf { v }\), determine the angle between the vectors \(\mathbf { u }\) and \(\mathbf { v }\), given that this angle is acute.