express the vector V as the sum of a vector parallel to B and a vector orthagonal to B
V=4i-2j+6k, B=-2i+j-3k
I got the orthognal as 7/3(-2i+j-3k)
but i dont understand the first part for the line of me!please help someone
1.You may have noticed that $\displaystyle \vec V = (-2) \cdot \vec B$ . That means $\displaystyle \vec V$ and $\displaystyle \vec B$ are collinear (or in simple terms: They are parallel).
2. Let $\displaystyle \vec N$ denote the vector orthogonal to $\displaystyle \vec B$ (by the way there are an unlimited number of such vectors!) then you have to determine $\displaystyle \vec N$:
$\displaystyle \vec V = (k) \cdot \vec B + \vec N$ with $\displaystyle k \in \mathbb{R}$
You'll get $\displaystyle \vec N = \vec 0$ where $\displaystyle \vec 0$ is the nullvector. (Per definition the nullvector is orthogonal to every vector)