Explain what is meant by scalar product and vector product.

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Solution

The scalar or dot product of two vectors can be calculated by taking the component of one vector in the direction of the other and multiplying it by the magnitude of the other vector. The dot product of two vectors yields a scalar quantity.
If we have two vectors $\to A$ and $\to B$ , their scalar product is given by
$\to A . \to B = | \to A | | \to B | cos θ$
Here, $| \to A |$ is the magnitude of $\to A$ .
$| \to B |$ is the magnitude of $\to B$ .
$θ$ is the angle between $\to A$ and $\to B$ .

The vector or cross product of two vectors yields a vector quantity.
If we have two vectors $\to A$ and $\to B$ , their vector product is given by a vector $\to C$ that is perpendicular to both $\to A$ and $\to B$ , with a direction given by the right-hand rule and the magnitude is
$| \to A \times \to B | = | \to A | | \to B | sin θ$
Here, $| \to A |$ is the magnitude of $\to A$ .
$| \to B |$ is the magnitude of $\to B$ .
$θ$ is the angle between $\to A$ and $\to B$ .

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