Question

Find a ⋅ b. a = 4i - 4j, b = 4i + 5j

-4
<8, 1>
<16, -20>
-36

Answer 1

a · b = a₁b₁ + a₂b₂ + ... = n

a · b = (4*4) + (-4*5) = 16 - 20 = -4

Answer 2

-4 is the answer to the product of two vectors.

Explanation:

We are given two vectors a and b such that:

a = 4i - 4j and b = 4i + 5j

Where i and j represent the unit vectors of x and y axis respectively with the property such that:

i.i= 1

i.j=0

j.i=0

j.j= 1

Now we are asked t find a.b

As a.b=(4i-4j)(4i+5j)

=4i×(4i)-4j×(4i)+4i×(5j)-4j×(5j)

=16i.i-16 i.j+20 i.j-20 j.j

= 16-0+0-20

= 16-20

= -4

Hence the value of a.b is -4.