Vector projection and perpendicular

Hi,

I am trying to solve the following problem:

1. Find the projection of on . Hence resolve into two vectors, one parallel to and the other perpendicular to .

I can solve the the first part, just by using the projection formula =

But how do I get it perpendicular to ? I know that if the dot product of two vectors = 0, then they are perpendicular. So:

projection dot ??? = 0. How do I calculate what to dot it with?

Re: Vector projection and perpendicular

By trial and error i+j-k is perpendicular to v

Re: Vector projection and perpendicular

What about uXv (croos product)?

Re: Vector projection and perpendicular

Quote:

Originally Posted by

**M.R** 1. Find the projection of

on

.

Hence resolve

into two vectors, one parallel to

and the other perpendicular to

.

I can solve the the first part, just by using the projection formula =

But how do I get it perpendicular to

?

You need to know these two:

Those two are perpendicular and their sum is .

Re: Vector projection and perpendicular

Quote:

Originally Posted by

**Plato**

That's what I needed. Thanks

Re: Vector projection and perpendicular

Quote:

Originally Posted by

**M.R** Hi,

I am trying to solve the following problem:

1. Find the projection of

on

. Hence resolve

into two vectors, one parallel to

and the other perpendicular to

.

I can solve the the first part, just by using the projection formula =

But how do I get it perpendicular to

? I know that if the dot product of two vectors = 0, then they are perpendicular. So:

projection dot ??? = 0. How do I calculate what to dot it with?

This is a more geometrical explanation (if I understand your problem correctly!):

The vectors und span a plane. You are looking for a vector which lies in this plane and is perpendicular to .

will do.

Re: Vector projection and perpendicular

Quote:

Originally Posted by

**earboth** This is a more geometrical explanation (if I understand your problem correctly!):

The vectors

und

span a plane. You are looking for a vector

which lies in this plane and is perpendicular to

.

will do.

Would that also mean that it is perpendicular to both vectors and ?

Re: Vector projection and perpendicular

Quote:

Originally Posted by

**M.R** Would that also mean that it is perpendicular to both vectors

and

?

Yes that is correct. The answer I gave you is a standard in as much as it is the decomposition of into the sum of two vectors one parallel to the other perpendicular to .

Re: Vector projection and perpendicular