IB Diploma · Mathematics Aa

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 $a = 6 \hat{i} - 2 \hat{j} + 5 \hat{k}$ and $b = 2 \hat{i} - 2 \hat{j} - 3 \hat{k}$ ?
What is the dot product of $a = 0 \hat{i} + 0 \hat{j} - 4 \hat{k}$ and $b = 5 \hat{i} - 3 \hat{j} + 3 \hat{k}$ ?
What is the dot product of $a = 3 \hat{i} - 3 \hat{j} + 5 \hat{k}$ and $b = 4 \hat{i} + 1 \hat{j} - 2 \hat{k}$ ?
What is the dot product of $a = 2 \hat{i} - 1 \hat{j} + 5 \hat{k}$ and $b = 4 \hat{i} - 1 \hat{j} + 0 \hat{k}$ ?
What is the dot product of $a = - 1 \hat{i} + 2 \hat{j} - 2 \hat{k}$ and $b = 4 \hat{i} + 1 \hat{j} - 4 \hat{k}$ ?
What is the dot product of $a = - 4 \hat{i} + 5 \hat{j} + 5 \hat{k}$ and $b = - 2 \hat{i} + 0 \hat{j} - 3 \hat{k}$ ?
What is the dot product of $a = - 1 \hat{i} + 3 \hat{j} - 4 \hat{k}$ and $b = - 1 \hat{i} + 5 \hat{j} - 4 \hat{k}$ ?
What is the dot product of $a = 0 \hat{i} + 6 \hat{j} - 3 \hat{k}$ and $b = 3 \hat{i} - 4 \hat{j} - 2 \hat{k}$ ?
What is the dot product of $a = 1 \hat{i} + 0 \hat{j} - 2 \hat{k}$ and $b = 4 \hat{i} - 4 \hat{j} - 3 \hat{k}$ ?
What is the dot product of $a = 0 \hat{i} + 4 \hat{j} + 1 \hat{k}$ and $b = 3 \hat{i} + 0 \hat{j} - 1 \hat{k}$ ?
A line has equation $r = 120 + t 2 - 1 2$ . What is the shortest distance from the point $P (4, 1, 5)$ to the line?
The lines $L_{1} : r = 102 + s 12 - 1$ and $L_{2} : r = - 2 0 p + t 213$ in…

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