Two vectors lying in the xy plane are given by the equations and . The value of is
A)19
B)−11
C)−19
D)11
E)10

Question

Two vectors lying in the xy plane are given by the equations  and  . The value of  is
A)19 
B)−11 
C)−19 
D)11 
E)10

Quizplus · Accepted Answer

We need to find the dot product of the given vectors. 
a · b = (5)(2) + (1)(-3) = 7 
Now we need to find the magnitude of the two given vectors. 
|a| = sqrt(5^2 + 1^2) = sqrt(26) 
|b| = sqrt(2^2 + (-3)^2) = sqrt(13) 
Thus, |a||b| = sqrt(338). 
Finally, we can find the angle between the two vectors using the formula: 
cos(theta) = a · b / (|a||b|) 
cos(theta) = 7 / sqrt(338) 
theta = acos(7 / sqrt(338))
theta ≈ 110.92°
Since the angle is greater than 90°, the dot product is negative. Thus, the answer is (C) -19.

Two Vectors Lying in the Xy Plane Are Given by the Equations