# Vector dot products

by mindheavy
Tags: products, vector
 P: 61 I'm reading up on dot products and keep seeing two different examples. One states that u$\cdot$v = u$_{i}$$\cdot$v$_{i}$ + u$_{j}$$\cdot$v$_{j}$ Another: u$\cdot$v = |u|$\cdot$|v|cosθ I'm not understanding when to use the first or second method?
 Quote by mindheavy I'm reading up on dot products and keep seeing two different examples. One states that u$\cdot$v = u$_{i}$$\cdot$v$_{i}$ + u$_{j}$$\cdot$v$_{j}$ Another: u$\cdot$v = |u|$\cdot$|v|cosθ I'm not understanding when to use the first or second method?
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 Vector dot products For example, if you are given that one vector is <1, 0, 0> and the other is <2, 2, 0> it is easy to calculate that the dot product is 1(2)+ 0(2)+ 0(0)= 2. But if you are given that one angle has length 1, the other has length $2\sqrt{2}$, and the angle between them is $\pi/4$, it is easiest to calculate $(1)(2\sqrt{2})(cos(\pi'4)= 2$. By the way, in spaces of dimension higher than 3, we can use the "sum of products of corresponding components" to find the dot product between two vectors, then use $|u||v|cos(\theta)$ to define the "angle between to vectors".