First slide

Vectors

Question

The angle between the two vectors $- 2 \hat{i} + 3 \hat{j} + \hat{k}$ and $\hat{i} + 2 \hat{j} - 4 \hat{k}$ is

Moderate

A

45°
B

90°
C

30°
D

60°

Solution

Let A = $- 2 \hat{i} + 3 \hat{j} + \hat{k}$
B = $\hat{i} + 2 \hat{j} - 4 \hat{k}$
$∴ A \cdot B = (- 2 \hat{i} + 3 \hat{j} + \hat{k}) \cdot (\hat{i} + 2 \hat{j} - 4 \hat{k})$
$= - 2 + 6 - 4 = 0$
Since, dot product of two vectors is zero, so vectors will be perpendicular (i.e. $θ$ = 90°) to each other.

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