# Math Help - Projections

1. ## Projections

If a b than a ↓ b = (a*b/(|b|^2))b and b ↓ a = (b*a/(|a|^2))a correct? If not, why will b ↓ a will still be (b*a/(|a|^2)) but with a multiple of b at the end? That is why my book is saying in the back. That it is still vector b as compared to vector a.

2. Originally Posted by Barthayn
If a b than a ↓ b = (a*b/(|b|^2))b and b ↓ a = (b*a/(|a|^2))a correct? If not, why will b ↓ a will still be (b*a/(|a|^2)) but with a multiple of b at the end? That is why my book is saying in the back. That it is still vector b as compared to vector a.
It appears that you are talking about projections
$a \downarrow b = \text{proj}_b a = \frac{{a \cdot b}}{{b \cdot b}}b$.

3. my question is if it is always b? An example is below:

Vectors a and b are such that |a| = 5, |b| = 3, and the angle between them is 150^o. Determine a ↓ b and b ↓ a.

The book claims it is (-(5*(3)^0.5)/6)*b and (-3(3)^0.5/10)b. Why is it two b and not b and then a?