[Dot Product] Vector Proection

[Highway]

[Dot Product] Vector Projection

Homework Statement

Homework Equations

The Attempt at a Solution

I am not sure what to do here -- I know that the projection of u onto a "dotted" with w = 0 by definition, but I don't know how to show this.

added this second part after plugging in for the definition of the projection we derived in class, then simplified. . .

 

[Highway]

anyone?

 

[I like Serena]

Hi Highway!

You have an expression for the projection.
Can you substitute that (and only that) in the formula you have for w?

To show that 2 vectors are orthogonal, you need to show that their dot product is zero. That is, that \vec a \cdot \vec w = 0.

What you need to know, is that there are calculation rules for dot products.
For instance \vec a \cdot (\vec b+\vec c) = \vec a \cdot \vec b + \vec a \cdot \vec c.

Can you simplify the expression for \vec a \cdot \vec w = 0?

 

[Highway]

Hi Highway!

You have an expression for the projection.
Can you substitute that (and only that) in the formula you have for w?

To show that 2 vectors are orthogonal, you need to show that their dot product is zero. That is, that \vec a \cdot \vec w = 0.

What you need to know, is that there are calculation rules for dot products.
For instance \vec a \cdot (\vec b+\vec c) = \vec a \cdot \vec b + \vec a \cdot \vec c.

Can you simplify the expression for \vec a \cdot \vec w = 0?

Thanks! I got it figured out :P

 

[I like Serena]

Congrats!