Cambridge A-Level · Mathematics

Vectors

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

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 12 questions

What is the dot product of $a = 1 \hat{i} + 1 \hat{j} + 2 \hat{k}$ and $b = 6 \hat{i} + 2 \hat{j} + 0 \hat{k}$ ?
What is the dot product of $a = 3 \hat{i} + 0 \hat{j} + 4 \hat{k}$ and $b = 2 \hat{i} - 3 \hat{j} - 1 \hat{k}$ ?
What is the dot product of $a = 3 \hat{i} + 6 \hat{j} - 1 \hat{k}$ and $b = 5 \hat{i} - 2 \hat{j} - 2 \hat{k}$ ?
What is the dot product of $a = 0 \hat{i} - 4 \hat{j} - 2 \hat{k}$ and $b = - 4 \hat{i} + 1 \hat{j} + 5 \hat{k}$ ?
What is the dot product of $a = 5 \hat{i} + 0 \hat{j} + 5 \hat{k}$ and $b = 6 \hat{i} + 5 \hat{j} + 4 \hat{k}$ ?
What is the dot product of $a = 0 \hat{i} + 1 \hat{j} + 4 \hat{k}$ and $b = - 2 \hat{i} - 2 \hat{j} - 1 \hat{k}$ ?
What is the dot product of $a = - 1 \hat{i} + 1 \hat{j} - 1 \hat{k}$ and $b = 4 \hat{i} + 0 \hat{j} - 3 \hat{k}$ ?
What is the dot product of $a = 6 \hat{i} - 2 \hat{j} + 5 \hat{k}$ and $b = 0 \hat{i} + 5 \hat{j} + 6 \hat{k}$ ?
What is the dot product of $a = 1 \hat{i} + 2 \hat{j} + 5 \hat{k}$ and $b = 5 \hat{i} + 0 \hat{j} + 4 \hat{k}$ ?
What is the dot product of $a = 1 \hat{i} + 5 \hat{j} + 6 \hat{k}$ and $b = 2 \hat{i} + 1 \hat{j} - 2 \hat{k}$ ?
$A$ , $B$ and $C$ have position vectors $2 - 1 3$ , $533$ and $77 - 1$ . What is angle $A B C$ , in degrees to $3$ …
A line has equation $r = 5 - 1 0 + t 212$ . What is the least distance from the origin to a point on the line?

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