Pre Calculus

Question

Determine the angle measure between vectors u and v: u = – i + 3j and v = 3i + j

a)180 degrees

b) 0 degrees

c) 90 degrees

d) 45 degrees

Answer 1

Vector u has a slope of  (3-0)/(-1-0) = -3.  Vector v has a slope of (1-0)/(3-0) = 1/3.  Since the slopes are negative reciprocals of another, the vectors are perpendicular.  So the answer is c) 90^o

 

To verify, take the dot product of u and v.  If the dot product is zero, the vectors are perpendicular:

 

u*v = (-1)*(3) + (3)*(1) = -3 + 3 = 0