What is the difference between the dot product and cross product of two vectors?

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Solution

Dot Product:
The dot product ( $\to a . \to b$ ) of two vectors $\to a$ and $\to b$ is a scalar quantity.

We can calculate the dot product as:
$\to a . \to b = | \to a | | \to b | c o s (θ)$
where:
Here, $| \to a |$ is the magnitude of vector $\to a$ .
$| \to b |$ is the magnitude of vector $\to b$ .
$θ$ is the angle between $\to a$ and $\to b$ .

Cross Product:
The cross product ( $\to a \times \to b$ ) of two vectors $\to a$ and $\to b$ is another vector that is at right angles to both these vectors.

We can calculate the cross product as:
$| \to a \times \to b | = | \to a | | \to b | s i n (θ)$
Here, $| \to a |$ is the magnitude of vector $\to a$ .
$| \to b |$ is the magnitude of vector $\to b$ .
$θ$ is the angle between $\to a$ and $\to b$ .
The direction is given by right-hand rule.

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