What is the unit vector of v: <-6, -8>?
sqrt(36 + 64) = sqrt 100 = 10
so that vector is ten units long.
If you divide each component by 10, you will get a vector of length one in that same direction so
< -6/10 , -8/10 >
or
< -3/5 , -4/5 >
by the way this is a 3,4,5 right triangle :)
To find the unit vector of a vector, you need to divide the vector by its magnitude.
In this case, the given vector is v = <-6, -8>.
Step-by-step process to find the unit vector:
1. Calculate the magnitude of vector v using the formula: ||v|| = sqrt(x^2 + y^2), where x and y are the components of the vector.
In this case, the magnitude is ||v|| = sqrt((-6)^2 + (-8)^2) = sqrt(36 + 64) = sqrt(100) = 10.
2. Divide each component of the vector by its magnitude:
The unit vector u of v is given by u = <x/magnitude, y/magnitude>, where x and y are the components of v and magnitude is the magnitude of v.
In this case, the unit vector u = <-6/10, -8/10> = <-0.6, -0.8>.
Therefore, the unit vector of v: <-6, -8> is <-0.6, -0.8>.