PRE-CAL HELPVector u has its initial point at (21, 12) and its terminal point at (19, -8). Vector v has a direction opposite that of u, whose magnitude is five times the magnitude of v. Which is the correct form of vector v expressed as a linear combination of the unit vectors i and j?

be
 P = (21, 12)
 Q = (19, -8).
 The vector u will be given by
 u = PQ = Q-P = (19, -8) - (21, 12) = (- 2, -20)
 The magnitude of this vector is
 u = ROOT ((2 ^ 2) + (20 ^ 2)) = 20.1
 Therefore, the vector v as it is in the opposite sense to u will be given by
 v = 0.4i + 4j.
  Its magnitude is
  v = Root((0.4^2)+(4^2))=4.02

 Dividing both magnitudes it is verified that the magnitude of u is five times greater than that of v
 20.1 / 4.02 = 5.
 Finally, the correct answer is
 v = 0.4i + 4j