JEE Main · Mathematics

Vectors

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

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What is the dot product of $a = 4 \hat{i} + 4 \hat{j} + 0 \hat{k}$ and $b = 2 \hat{i} + 3 \hat{j} - 1 \hat{k}$ ?
What is the dot product of $a = - 3 \hat{i} + 6 \hat{j} + 0 \hat{k}$ and $b = 1 \hat{i} - 1 \hat{j} + 3 \hat{k}$ ?
What is the dot product of $a = 3 \hat{i} + 0 \hat{j} - 1 \hat{k}$ and $b = 3 \hat{i} + 3 \hat{j} + 4 \hat{k}$ ?
What is the dot product of $a = 3 \hat{i} + 0 \hat{j} + 6 \hat{k}$ and $b = - 1 \hat{i} - 1 \hat{j} + 3 \hat{k}$ ?
What is the dot product of $a = 1 \hat{i} + 2 \hat{j} - 1 \hat{k}$ and $b = 6 \hat{i} + 3 \hat{j} + 4 \hat{k}$ ?
What is the dot product of $a = - 4 \hat{i} + 4 \hat{j} + 6 \hat{k}$ and $b = - 2 \hat{i} - 1 \hat{j} + 1 \hat{k}$ ?
What is the dot product of $a = 6 \hat{i} + 3 \hat{j} + 3 \hat{k}$ and $b = - 2 \hat{i} + 0 \hat{j} + 1 \hat{k}$ ?
What is the dot product of $a = - 1 \hat{i} + 0 \hat{j} - 2 \hat{k}$ and $b = - 2 \hat{i} + 0 \hat{j} - 1 \hat{k}$ ?
What is the dot product of $a = - 4 \hat{i} + 3 \hat{j} + 3 \hat{k}$ and $b = - 4 \hat{i} + 0 \hat{j} + 5 \hat{k}$ ?
What is the dot product of $a = - 1 \hat{i} - 1 \hat{j} + 1 \hat{k}$ and $b = - 1 \hat{i} - 2 \hat{j} - 2 \hat{k}$ ?
What is the dot product of $a = 2 \hat{i} + 2 \hat{j} - 3 \hat{k}$ and $b = 6 \hat{i} - 4 \hat{j} - 2 \hat{k}$ ?
What is the dot product of $a = 3 \hat{i} + 1 \hat{j} + 0 \hat{k}$ and $b = 6 \hat{i} + 2 \hat{j} + 0 \hat{k}$ ?
What is the dot product of $a = 3 \hat{i} - 3 \hat{j} + 0 \hat{k}$ and $b = - 4 \hat{i} - 4 \hat{j} + 0 \hat{k}$ ?
What is the dot product of $a = - 3 \hat{i} + 4 \hat{j} + 4 \hat{k}$ and $b = 5 \hat{i} - 2 \hat{j} + 1 \hat{k}$ ?
What is the dot product of $a = 3 \hat{i} + 0 \hat{j} + 3 \hat{k}$ and $b = 2 \hat{i} - 1 \hat{j} + 3 \hat{k}$ ?
What is the dot product of $a = 4 \hat{i} + 6 \hat{j} + 0 \hat{k}$ and $b = 6 \hat{i} + 0 \hat{j} - 1 \hat{k}$ ?
What is the dot product of $a = - 2 \hat{i} - 3 \hat{j} + 6 \hat{k}$ and $b = - 4 \hat{i} + 4 \hat{j} - 2 \hat{k}$ ?
What is the dot product of $a = 4 \hat{i} - 1 \hat{j} - 1 \hat{k}$ and $b = - 3 \hat{i} + 0 \hat{j} - 1 \hat{k}$ ?
What is the dot product of $a = 6 \hat{i} - 3 \hat{j} - 4 \hat{k}$ and $b = - 1 \hat{i} + 1 \hat{j} + 3 \hat{k}$ ?
What is the dot product of $a = 0 \hat{i} - 4 \hat{j} + 4 \hat{k}$ and $b = - 3 \hat{i} - 1 \hat{j} - 2 \hat{k}$ ?
What is the dot product of $a = 0 \hat{i} + 2 \hat{j} + 3 \hat{k}$ and $b = 6 \hat{i} - 1 \hat{j} - 4 \hat{k}$ ?
What is the dot product of $a = - 4 \hat{i} + 3 \hat{j} - 4 \hat{k}$ and $b = 3 \hat{i} + 5 \hat{j} + 6 \hat{k}$ ?
What is the dot product of $a = - 4 \hat{i} + 5 \hat{j} + 5 \hat{k}$ and $b = - 2 \hat{i} + 2 \hat{j} + 1 \hat{k}$ ?
What is the dot product of $a = - 3 \hat{i} - 1 \hat{j} + 5 \hat{k}$ and $b = - 2 \hat{i} + 2 \hat{j} + 5 \hat{k}$ ?
What is the dot product of $a = - 1 \hat{i} + 2 \hat{j} + 4 \hat{k}$ and $b = 2 \hat{i} - 2 \hat{j} + 5 \hat{k}$ ?
What is the perpendicular distance of the point $P (5, - 3, 1)$ from the line $\frac{x - 1}{1} = \frac{y - 2}{- 2} = \frac{z + 1}{2}$ ?
What is the shortest distance between the lines $r = (i + 3 k) + s (2 i + j + 2 k)$ and…
Vectors $a, b$ satisfy $∣ a ∣ = 3, ∣ b ∣ = 4$ and $a \cdot b = 6$ . What is $∣ (a + 2 b) \times (2 a - b) ∣$ ?
$a$ and $b$ are unit vectors with angle $6 0^{\circ}$ between them. The value of $(a + 2 b) \times (2 a - b)$ is

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