Question

How do you multiply vectors by vectors$?$

Answer 1

We have two different methods to multiply vectors by vectors. They are:

$1)$ Cross product

$2)$ Dot product

$1)$Cross product (vector product) of two vectors is equal to the product of the magnitude of vectors and sine of the angle formed between them.

If$A$ and$B$ are two vectors, then the cross product of$A$ and$B$ is given by:

$\overrightarrow{A}\times \overrightarrow{B}=\left|A\right|\left|B\right|\sin \theta \hat{n}$

where $\hat{n}$ is the unit vector, in the direction of $\overrightarrow{A}\times \overrightarrow{B}$ and perpendicular to $\overrightarrow{A}$ and $\overrightarrow{B}$

$2)$Dot Product (scalar product) is the product of the magnitude of vectors and the cosine of the angle formed between them. If$A$ and $B$ are two vectors, then the dot product of $A$ and$B$ is given by:

$\overrightarrow{A}.\overrightarrow{B}=\left|A\right|\left|B\right|\cos \theta$