Define vector product of two vectors. - Vidyadip

Question

Define vector product of two vectors.

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Answer

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two non-zero non-parallel vectors, then the vector product denoted by $\vec{\text{a}}\times\vec{\text{b}}$ is defined as $\vec{\text{a}}\times\vec{\text{b}}=|\vec{\text{a}}|\big|\vec{\text{b}}\big|\sin\theta\eta.$
Here, $\theta$ is the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$ and $\eta$ is
the unit vector perpendicular to the plane of $\vec{\text{a}}$ and $\vec{\text{b}}$ such that $\vec{\text{a}},\vec{\text{b}}$ and $\eta$ from a right handed system.

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