cross product(vectors)

Country_boy_88 · #1 $Old$ 08-28-2008, 10:05 PM

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

earboth · #2 $Old$ 08-28-2008, 10:55 PM

Quote:

Originally Posted by Country_boy_88 $View Post$

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 $\vec V = (-2) \cdot \vec B$ . That means $\vec V$ and $\vec B$ are collinear (or in simple terms: They are parallel).

2. Let $\vec N$ denote the vector orthogonal to $\vec B$ (by the way there are an unlimited number of such vectors!) then you have to determine $\vec N$ :

$\vec V = (k) \cdot \vec B + \vec N$ with $k \in \mathbb{R}$

You'll get $\vec N = \vec 0$ where $\vec 0$ is the nullvector. (Per definition the nullvector is orthogonal to every vector)