vectors that are parallel to projections

[seven]

1.) Which vector is always orthogonal to b−proja onto b

a.) vector a

b.) vector b

c.) vector a - vector b

d.) mag(a)*b

e.) projb onto a

 

[lev888]

b−proja onto b

What?

 

[seven]

What?

vector b minus projection of a onto b
hence "b−proja onto b"

 

[Dr.Peterson]

1.) Which vector is always orthogonal to b−proja onto b

a.) vector a

b.) vector b

c.) vector a - vector b

d.) mag(a)*b

e.) projb onto a

I suspect you may be confusing the notation. The question makes most sense if your "b−proja onto b" is taken as "b - proj_a(b)", that is, b minus the projection ONTO a OF b.

Please show us the actual problem, and tell us your thoughts on it, so we can see where you need help.

 

[pka]

1.) Which vector is always orthogonal to b−proja onto b

a.) vector a

b.) vector b

c.) vector a - vector b

d.) mag(a)*b

e.) projb onto a

You have greatly confused this question.
The projection of \(\displaystyle \vec{a}\text{ onto }\vec{b}\;\;\text{ is }\;\;\left( \frac{\vec{a}\cdot\vec{b}}{\vec{b}\cdot\vec{b}}\right)\large\vec{b}\)
Now rethink your answers. The \(\displaystyle \text{proj}(\vec{v}\text{ onto }\vec{w})\) is a vector that is parallel to \(\displaystyle \vec{w}\).