# What is the dot product of <3,-7,6 > and <4,1,7 >?

Jan 28, 2016

The dot product of two vectors, also called the 'scalar product' is a single number, in this case $47$.

#### Explanation:

To find the dot product (scalar product) of two vectors $\left[{a}_{1} , {a}_{2} , {a}_{3} , \ldots , {a}_{n}\right]$ and $\left[{b}_{1} , {b}_{2} , {b}_{3} , \ldots , {b}_{n}\right]$, we simply multiply the corresponding elements and add all the products:

${a}_{1} {b}_{1} + {a}_{2} {b}_{2} + {a}_{3} {b}_{3} + \ldots . + {a}_{n} {b}_{n}$

In this case, the dot product is:

$3 \cdot 4 + \left(- 7\right) \cdot 1 + 6 \cdot 7 = 12 - 7 + 42 = 47$