Solve the problem.
-If u =-5, 3 , v =6, -6 , and w =-3, 12, evaluate u ·w + v ·w.
A) -39
B) -34
C) -32
D) -43

Question

Quizplus · Accepted Answer

The dot product of two vectors $ \mathbf{a} = (a_1, a_2) $ and $ \mathbf{b} = (b_1, b_2) $ is given by $ \mathbf{a} \cdot \mathbf{b} = a_1b_1 + a_2b_2 $. For $ \mathbf{u} \cdot \mathbf{w} $, we have $ (-5)(-3) + (3)(12) = 15 + 36 = 51 $. For $ \mathbf{v} \cdot \mathbf{w} $, we have $ (6)(-3) + (-6)(12) = -18 - 72 = -90 $. Adding these results gives $ 51 + (-90) = -39 $.

Solve the Problem. -If U =-5, 3 , V =6, -6 , and -6