Question

I am asked to find the vector component of v along b and the vector orthogonal to b. Could someone please help provide formulas to solve these problems or just help in general?
Thanks...

Answer 1

Is that a linear algebra problem? Have you learned the inner product?

Answer 2

Calc III

Answer 3

Say the vector that is orthogonal to b is x. Then the inner/dot product of b and x will be zero. I don't know if this can help.

Answer 4

@giolefpatceid it applies linear algebra to cal 3, the same formula

Answer 5

\[proj_a u=\frac{u(dot)a}{||a||^2}a\]

Answer 6

which component does that formula provide?

Answer 7

It provides the orthogonal projection, yes?

How do I find the vector component of v along b then?

Answer 8

@loser66

Answer 9

@e.mccormick explain him, please

Answer 10

from my formula, it calculate vector u along a , you just replace u =v and a =b so you have vector v along b, does it make sense?

Answer 11

ok then how do I find the vector component orthogonal to b?

Answer 12

A projection is short for Orthogonal Projection.

Answer 13

This has a good example of how that formula is made and a diagram of what it represents:
http://www.math4all.in/public_html/linear%20algebra/chapter8.1.html

Answer 14

@loser
my book says that the formula you provided me defines the orthogonal projection of v on vector b.

Answer 15

Does your book talk about subtracting the projection from the vector to get the component that is orthogonal?

Answer 16

ok yes I got it now...the way my book explained this is a bit misleading to me...thanks for the help.

Answer 17

Something like this? Find the vector component \(\vec{w}\) of \(\vec{u}\) orthogonal to \(\vec{v}\):
\( w = u - \cfrac{{u \cdot v}}{{v \cdot v}}v\)

Answer 18

If you ever run into the Ghram-Schmidt Orthornormalization, you will see some of this pop up again.

Answer 19

ok thanks