First slide

Vectors

Question

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

Moderate

A

obtuse
B

right angle
C

acute
D

can't say

Solution

Let $\vec{A} = - 2 \hat{i} + 3 \hat{j} + \hat{k} \vec{B} = 2 \hat{i} + 2 \hat{j} - 4 \hat{k}$
$\vec{A} \vec{. B} = - 2 \times 2 + 3 \times 2 + 1 \times (- 4) = - 2$
Since dot product is negative, so angle between vectors is obtuse.

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