GATE · Engineering Mathematics

Vectors

10 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 10 questions

What is the dot product of $a = - 4 \hat{i} - 3 \hat{j} - 1 \hat{k}$ and $b = - 1 \hat{i} + 3 \hat{j} + 0 \hat{k}$ ?
What is the dot product of $a = - 4 \hat{i} + 4 \hat{j} - 3 \hat{k}$ and $b = - 3 \hat{i} - 1 \hat{j} + 5 \hat{k}$ ?
What is the dot product of $a = 3 \hat{i} + 1 \hat{j} - 1 \hat{k}$ and $b = - 3 \hat{i} - 3 \hat{j} + 2 \hat{k}$ ?
What is the dot product of $a = 4 \hat{i} + 1 \hat{j} + 5 \hat{k}$ and $b = - 1 \hat{i} + 1 \hat{j} + 4 \hat{k}$ ?
What is the dot product of $a = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ and $b = 3 \hat{i} + 5 \hat{j} - 3 \hat{k}$ ?
What is the dot product of $a = 5 \hat{i} + 0 \hat{j} - 4 \hat{k}$ and $b = 2 \hat{i} + 6 \hat{j} - 3 \hat{k}$ ?
What is the dot product of $a = - 1 \hat{i} - 4 \hat{j} - 1 \hat{k}$ and $b = - 3 \hat{i} + 1 \hat{j} - 3 \hat{k}$ ?
What is the dot product of $a = 1 \hat{i} - 2 \hat{j} + 5 \hat{k}$ and $b = 4 \hat{i} + 3 \hat{j} + 3 \hat{k}$ ?
What is the dot product of $a = - 2 \hat{i} + 5 \hat{j} + 2 \hat{k}$ and $b = - 4 \hat{i} - 4 \hat{j} + 1 \hat{k}$ ?
What is the dot product of $a = - 4 \hat{i} + 4 \hat{j} + 1 \hat{k}$ and $b = 5 \hat{i} - 1 \hat{j} - 2 \hat{k}$ ?

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