- #1

- 9

- 0

## Homework Statement

I get confused with this problems

show that the vector (orth of b onto a) = (b - proj of b onto a) is orthogonal to a.

## Homework Equations

## The Attempt at a Solution

(b-proj of b onto a) dot a = 0

and I got stuck!

- Thread starter baokhuyen
- Start date

- #1

- 9

- 0

I get confused with this problems

show that the vector (orth of b onto a) = (b - proj of b onto a) is orthogonal to a.

(b-proj of b onto a) dot a = 0

and I got stuck!

- #2

matt grime

Science Advisor

Homework Helper

- 9,395

- 3

Perhaps if you wrote out what "proj of b onto a" was in vector terms it would become easier.

- #3

- 9

- 0

For example, I say:

(b- a(a.b)/a^2).a=0

(b-(a.b)/a).a=0

a.b-a.((a.b)/a)=0

How can I do next?

(b- a(a.b)/a^2).a=0

(b-(a.b)/a).a=0

a.b-a.((a.b)/a)=0

How can I do next?

- #4

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

You are not being careful to distinguish between vectors and numbers. The first "a" of "a(a.b)/a^2" is a vector while "a^2" is a number- the square of the length of a. You are trying to cancel them!For example, I say:

(b- a(a.b)/a^2).a=0

with the result that you get this, which makes no sense! Does "(a.b)/a" mean you are(b-(a.b)/a).a=0

[tex]\left(\vec{b}- \frac{\vec{a}\cdot\vec{b}}{|a|^2}\vec{a}\right)\cdot\vec{a}[/tex]a.b-a.((a.b)/a)=0

How can I do next?

[tex]\vec{b}\cdot\vec{a}- \frac{\vec{a}\cdot\vec{b}}{|a|^2}(\vec{a}\cdot\vec{a})[/tex]

Now, what is that equal to?

- Last Post

- Replies
- 5

- Views
- 1K

- Last Post

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 7

- Views
- 4K

- Last Post

- Replies
- 11

- Views
- 2K

- Last Post

- Replies
- 12

- Views
- 1K

- Last Post

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 1K

- Last Post

- Replies
- 7

- Views
- 3K

- Replies
- 7

- Views
- 1K

- Replies
- 16

- Views
- 2K