First slide

Vectors

Question

${\hat{u}}_{1}, {\hat{u}}_{2} and {\hat{u}}_{3}$ are three unit vector such that ${\hat{u}}_{1} + {\hat{u}}_{2} + {\hat{u}}_{3} = 0$ . Then the value of $({\hat{u}}_{1} . {\hat{u}}_{2} - 4 {\hat{u}}_{3} . {\hat{u}}_{1})$ is

Moderate

A

1.5
B

2.5
C

0.5
D

Zero

Solution

Since ${\hat{u}}_{1} + {\hat{u}}_{2} + {\hat{u}}_{3} = 0$ , they must form a closed triangle as shown.
$\begin{array}{l} ∴ {\hat{u}}_{1} . {\hat{u}}_{2} - 4 {\hat{u}}_{3} . {\hat{u}}_{1} \\ = 1 .1. \cos 120^{0} - 4 .1.1 \cos 120^{0} \\ = - \frac{1}{2} + 2 = 1 .5 \end{array}$

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