# Consider the following vectors: v = 3i + 4j, w = 4i + 3j, how do you find the dot product v·w?

##### 1 Answer
Jan 5, 2016

$24$

#### Explanation:

Definition : Let $v = \left({v}_{1} , {v}_{2} , \ldots . , {v}_{n}\right) \mathmr{and} w = \left({w}_{1} , {w}_{2} , \ldots , {w}_{n}\right)$ be any 2 vectors in ${\mathbb{R}}^{n} \mathmr{and} {\mathbb{C}}^{n}$.
Then the Euclidean inner product (also called dot product) of $v$ with $w$is a real or complex number defined by
$v \cdot w = {v}_{1} {w}_{1} + {v}_{2} {w}_{2} + \ldots . . + {v}_{n} {w}_{n}$.

So in this particular case we work in ${\mathbb{R}}^{2}$ and get,

$\left(3 , 4\right) \cdot \left(4 , 3\right) = \left(3 \times 4\right) + \left(4 \times 3\right) = 12 + 12 = 24 \in \mathbb{R}$.