Question

Vector A= 3.7 i + 1.0 j and vector B = 3.0 i + 6.5 j. What is vector (A-B).A?

Answer 1

Answer:

(A - B).A = -2.91

Explanation:

First, let's define the sum and dot product of vectors.

For two vectors V = (x₁, y₁) and W = (x₂, y₂) we have:

sum (or subtraction):

V + W = (x₁, y₁) +  (x₂, y₂)  = (x₁ + x₂, y₁ + y₂)

dot product:

V.W =  (x₁, y₁).(x₂, y₂) = x₁*x₂ + y₁*y₂

Here remember the notation:

V = x₁*i + y₁*j =  (x₁, y₁)

Now let's solve our problem, we have:

A = (3.7, 1.0)

B = (3.0, 6.5)

Then:

(A - B).A = (  (3.7, 1.0) -  (3.0, 6.5) ).(3.7, 1.0)

              = (3.7 - 3.0, 1.0 - 6.5).(3.7, 1.0)

              = (0.7, -5.5).(3.7, 1.0) = (0.7*3.7) + (-5.5)*(1.0) = -2.91