Singapore GCE A-Level · H2 Mathematics

Vectors in 3D Space and Complex Numbers

6 practice questions, each with the answer and an explanation.

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All 6 questions

Find the Cartesian equation of the plane passing through the point $(1, 2, - 1)$ with normal vector $n = 2 - 3 4$ .
Let $z = - 1 + i 3$ . Express $z$ in polar exponential form $r e^{i θ}$ where $- π < θ \leq π$ .
Find the vector cross product $a \times b$ where $a = 123$ and $b = 456$ .
Find the perpendicular distance from the point $P (2, 1, 4)$ to the plane $Π : x + 2 y - 2 z = 5$ .
If $w$ is a non-real root of $z^{3} = 1$ , find the value of $(1 + w) (1 + w^{2})$ .
The line $l$ has equation $r = 10 - 1 + λ 21 - 2$ . The plane $p$ has equation $2 x - y + z = 4$ . Find the acute angle…

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