First slide

Cross product of vectors or vector product of vectors

Question

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} \cdot \vec{b} = 0 = \vec{a} \cdot \vec{c}$ and the angle between $\vec{b} and \vec{c} is π / 3$ the value of $| \vec{a} \times \vec{b} - \vec{a} \times \vec{c} |$ is

Moderate

A

$\frac{1}{2}$
B

1
C

2
D

none of these

Solution

$|\bar{a} \times (\bar{b} - \bar{c})| = |\bar{a}| |\bar{b} - \bar{c}| \sin (\bar{a}, (\bar{b} - \bar{c})) = \sqrt{{|b|}^{2} + {|c|}^{2} - 2 |b| |c| \cos \frac{π}{3}} \sin \frac{π}{2} (∵ (\bar{a}, (\bar{b} - \bar{c})) = \frac{π}{2}) = \sqrt{1 + 1 - 2 (\frac{1}{2})} = 1$

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