Question

Find a ⋅ b. a = 4i - 4j, b = 4i + 5j

Answer 1

`a \cdot \: b = - 4`

EXPLANATION

The dot product of two vectors

`a = xi + yj`

and

`b = mi + nj`

is given by

`a \cdot \: b = mx + ny`

The given vectors are:

`a = 4i - 4j`

`b = 4i + 5j`

Applying the above definition of dot products, we obtain:

`a \cdot \: b = 4 * 4 + - 4 * 5`

`a \cdot \: b = 16 - 20`

`a \cdot \: b = - 4`

Answer 2

value of a.b = -4

Explanation:

We need to find a.b

a= 4i-4j

b = 4i+5j

We know that i.i =1, j.j=1, i.j =0 and j.i=0

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

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

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

a.b = 16(1) +20(0)-16(0)-20(1)

a.b = 16 +0-0-20

a.b = 16-20

a.b =-4

So, value of a.b = -4