First slide

Cross product of vectors or vector product of vectors

Question

$If \bar{a} \times \bar{b} = \bar{c} and \bar{b} \times \bar{c} = \bar{a} then$

Difficult

A

$| \bar{a} | = 1$
B

$| \bar{b} | = 1$
C

$| \bar{a} | = | \bar{c} |$
D

$| \bar{b} | = | \bar{c} |$

Solution

$\bar{a} \times \bar{b} = \bar{c} \Rightarrow \bar{c} is perpendicular to \bar{a} and \bar{b}$
$\bar{b} \times \bar{c} = \bar{a} \Rightarrow \bar{a} is perpendicular to \bar{b} and \bar{c}$
$\Rightarrow \bar{a}, \bar{b}, \bar{c} are mutually perpendicular$
$Again \bar{a} \times \bar{b} = \bar{c} \Rightarrow | \bar{a} \times \bar{b} | = | \vec{c} | \Rightarrow | \bar{a} | | \bar{b} | = | \vec{c} | \to (1)$
$\bar{b} \times \bar{c} = \bar{a} \Rightarrow | \bar{b} \times \bar{c} | = | \bar{a} | \Rightarrow | \bar{b} | | \bar{c} | = | \bar{a} | \to (2) ∣$
$∴ From (1) & (2) | \bar{c} | = | \bar{a} | & | \bar{b} | = 1$

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