First slide

Vectors

Question

If $A = \hat{i} + \hat{j} + \hat{k}$ and $B = - \hat{i} - \hat{j} - \hat{k}$ , then what is the angle made by (A - B) with A?

Moderate

A

0°
B

180°
C

90°
D

60°

Solution

$A - B = (\hat{i} + \hat{j} + \hat{k}) - (- \hat{i} - \hat{j} - \hat{k})$
$= 2 \hat{i} + 2 \hat{j} + 2 \hat{k} = 2 A$
i.e. A $-$ B and A are parallel.
Hence, $θ$ = 0°

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