# How do you compute the dot product for u=4i-2j and v=i-j?

Sep 30, 2016

u•v = 6

#### Explanation:

For any two vectors ,u and v, of the form:

$\left({u}_{i}\right) \hat{i} + \left({u}_{j}\right) \hat{j}$

and

$\left({v}_{i}\right) \hat{i} + \left({v}_{j}\right) \hat{j}$

u•v = (u_i)(v_i) + (u_j)(v_j)

Substituting the given values:

u•v = (4)(1) + (-2)(-1)

u•v = 6

Note: For 3 dimensions the dot product extends to:

u•v = (u_i)(v_i) + (u_j)(v_j) + (u_k)(v_k)