What are scalar multiples and projections in vector operations?

[lypaza]

[PLAIN]http://img62.imageshack.us/img62/5319/49966749.png

What is the scalar multiples of a vector actually?
I was thinking L = c[2 1 2]^T
Then I looked for projection of v on L. But I got c in my answers which are not supposed to be...

 

[Mark44]

[PLAIN]http://img62.imageshack.us/img62/5319/49966749.png

What is the scalar multiples of a vector actually?
I was thinking L = c[2 1 2]^T
Then I looked for projection of v on L. But I got c in my answers which are not supposed to be...

Every vector in L is some scalar multiple of <2, 1, 2>. The line goes through the origin - the zero multiple of this vector is 0<2, 1, 2> = <0, 0, 0>, a vector that starts and ends at the origin. The line goes through the point (-4, -2, -4), which you can get by taking the -2 multiple of the vector.

For the reflection of v in the line, you want to find another vector w that is in the same plane as v and L, but is on the opposite side of L, and makes the same angle with L.

 

[lypaza]

So I have to find angle theta between v and L, and then find vector w with negative theta?
I also have to find the plane of v and L by cross product of v and L ...