2024 H2 Mathematics Paper 1 Question 2

Vectors I: Basics, Dot and Cross Products

Answers

$\sin θ = 1.$

$𝐚$ is a unit vector $\Rightarrow | 𝐚 | = 1$

\begin{array}{r} 𝐛 \cdot 𝐛 = 9 \\ {| 𝐛 |}^{2} = 9 \\ | 𝐛 | = 3 \end{array}

Let $θ$ be the angle between $𝐚$ and $𝐛 .$

\begin{matrix} | 𝐚 \times 𝐛 | = 3 \\ | 𝐚 | | 𝐛 | \sin θ = 3 \\ (1) (3) \sin θ = 3 \\ \sin θ = 1 \\ θ = 90^{\circ} \end{matrix}

Hence $𝐚$ and $𝐛$ are perpendicular $∎$