Find the unit vector that is parallel to but has opposite direction as the vector m=<-1,0,2,2>
MathMate did this for you
http://www.jiskha.com/display.cgi?id=1328502296
To find the unit vector that is parallel to a given vector, but has the opposite direction, you can follow these steps:
1. Find the magnitude of the given vector.
- The magnitude of a vector m = <a, b, c, d> is given by |m| = sqrt(a^2 + b^2 + c^2 + d^2).
For the given vector m = <-1, 0, 2, 2>:
- |m| = sqrt((-1)^2 + 0^2 + 2^2 + 2^2) = sqrt(1 + 0 + 4 + 4) = sqrt(9) = 3.
2. Divide each component of the given vector by its magnitude to get the direction.
- Let's denote the unit vector as u = <x, y, z, w>.
- To get u, divide each component of m by |m|: u = <-1/3, 0/3, 2/3, 2/3>.
Therefore, the unit vector that is parallel to but has the opposite direction as the vector m = <-1, 0, 2, 2> is u = <-1/3, 0, 2/3, 2/3>.