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Question
Tue October 25, 2011 By:

# What do you mean by a dot product ? How to find the dot product of two vectors ? Please explain .

Tue October 25, 2011

The scalar product of the two vectors. $\displaystyle{\vec{{A}}}$ and $\displaystyle{\vec{{B}}}$ is defined as the product of the magnitudes of the vectors $\displaystyle{\vec{{A}}}$ and $\displaystyle{\vec{{B}}}$ and the cosine of the angle between them.

The scalar or dot product of the two vectors $\displaystyle{\vec{{A}}}$ and $\displaystyle{\vec{{B}}}$ gives a scalar and is denoted as $\displaystyle{\vec{{A}}}$ $\displaystyle\cdot$ $\displaystyle{\vec{{B}}}$ ( read as $\displaystyle{\vec{{A}}}$ dot $\displaystyle{\vec{{B}}}$dot product or inner product of the two vectors. ). It is also known as

Mathematically if  $\displaystyle\theta$ is the angle between the vectors $\displaystyle{\vec{{A}}}$ and $\displaystyle{\vec{{B}}}$ in above figure then

$\displaystyle{\vec{{A}}}$ $\displaystyle\cdot$ $\displaystyle{\vec{{B}}}$  = A B cos$\displaystyle\theta$

The above equation can be written as $\displaystyle{\vec{{A}}}$ $\displaystyle\cdot$ $\displaystyle{\vec{{B}}}$ = A ( B cos$\displaystyle\theta$ ) = B (A cos$\displaystyle\theta$ )

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