SOLUTION: Let vector v=<5,-1,4>. Give a vector w in the opposite direction of v and with magnitude twelve. Give its components to the nearest tenth. I don't understand how to solve the probl

Algebra ->  Vectors -> SOLUTION: Let vector v=<5,-1,4>. Give a vector w in the opposite direction of v and with magnitude twelve. Give its components to the nearest tenth. I don't understand how to solve the probl      Log On


   

Question 286948: Let vector v=<5,-1,4>. Give a vector w in the opposite direction of v and with magnitude twelve. Give its components to the nearest tenth. I don't understand how to solve the problem and I can't seem to find any similar examples in the text.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
to get the opposite direction, change the signs of the components

w = <-5k, 1k, -4k>
the "k" is the factor to make the magnitude of w equal 12

the magnitude is the length of the vector
___ found by using the Pythagorean theorem on the components
___ m^2 = x^2 + y^2 + z^2

144 = 25k^2 + k^2 + 16k^2 = 42k^2

k = sqrt(144/42) = 1.852 (approx)

plug in the value of k to find the components of w