Dot product also known as Scalar product is the product of the two vectors got by operating the components of the vectors. The symbol of dot product is big dot (.). Consider two vector $\vec{x}$ and $\vec{y}$ where
$\vec{x}$ = a i + b j + c k
$\vec{y}$ = d i + e j + f k

The dot product formula for 3D is given by
Where a, b, c, d, e, f are the magnitudes of the components i, j, k of given vectors respectively.

Dot product Calculator calculates the dot product of given two vectors is a online tool which gives you the dot product instantly. Provided are the space where you are supposed to enter the magnitude of the components i, j and k to get the answer.

## Dot Product Examples

Step 1: Read the given problem and note down the given vectors

Step 2: Using dot product formula we have  x.y = ( ad + be + cf )

Substituting the magnitude of the given vector we get the answer.

Below are given some solved problems on dot product. You can go through it.

### Solved Examples

Question 1: Find the dot product of $\vec{x}$ = 3i + 3j + 5k and $\vec{y}$ = i - j + k.
Solution:

Step 1 : The given vectors are
$\vec{x}$ = 3i + 3j + 5k
$\vec{y}$ = i - j + k

Step 2 : The dot product is given by
x.y = (3i + 3j + 5k).(i - j + k)
= ((3)(1) + (3)(-1) + (5)(1))
= 3 - 3 + 5
= 5.

Question 2: Find the dot product of $\vec{x}$ = i + 8k and $\vec{y}$ = k.
Solution:

Step 1 : The given vectors are
$\vec{x}$ = i + 8k
$\vec{y}$ = k.

Step 2 : The dot product is given by
x.y = (i + 8k).(k)
= ((1)(0) + (0)(0) + (8)(1))
= 0 + 0 + 8
= 8.

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