Take this Quiz: A-Level Maths: Vectors | Zestly

Question 1

Given the vector $\mathbf{a} = 3\mathbf{i} - 4\mathbf{j} + 12\mathbf{k}$, what is the magnitude of this vector?

Accepted Answer

$13$

Question 2

Which of the following vectors are parallel to the vector $\mathbf{v} = 2\mathbf{i} - 6\mathbf{j} + 4\mathbf{k}$?

Accepted Answer

$\mathbf{i} - 3\mathbf{j} + 2\mathbf{k}$

Question 3

Points A and B have position vectors $\mathbf{a} = 2\mathbf{i} + 5\mathbf{j}$ and $\mathbf{b} = 8\mathbf{i} - 3\mathbf{j}$. What is the vector $\vec{AB}$?

Accepted Answer

$6\mathbf{i} - 8\mathbf{j}$

Question 4

Given points $P(1, 2, 3)$ and $Q(4, 5, 6)$, which of the following statements are true regarding the line segment $PQ$?

Answer

The midpoint is $(2.5, 3.5, 4.5)$

Answer

The vector $\vec{PQ}$ is $5\mathbf{i} + 7\mathbf{j} + 9\mathbf{k}$

Answer

The distance $PQ$ is $\sqrt{27}$

Answer

The midpoint is $(5, 7, 9)$

Question 5

A particle moves with constant velocity $\mathbf{v} = 3\mathbf{i} - 4\mathbf{j} 	ext{ m/s}$. If it starts at the origin, what is its position vector after 5 seconds?

Answer

$3\mathbf{i} - 4\mathbf{j}$

Answer

$15\mathbf{i} - 20\mathbf{j}$

Answer

$8\mathbf{i} - 9\mathbf{j}$

Answer

$15\mathbf{i} + 20\mathbf{j}$