Question

Find a ·
b. |a| = 80, |b| = 50, the angle between a and b is 3π/4.

Answer 1

a•b = |a|·|b|·cos(α)
= 80·50·cos(3π/4) = -2000√2

Answer 2

`a\cdot b=-2000√(2)`

Explanation:

Given information: |a| = 80, |b| = 50, the angle between a and b is 3π/4.

We need to find the dot product a · b.

The formula of dot product is

`a\cdot b=|a||b|\cos \theta`

where, θ is the angle between a and b.

Substitute the given values in the above formula.

`a\cdot b=(80)(50)\cos ((3\pi)/(4))`

`a\cdot b=4000\cos (\pi-(\pi)/(4))`

`a\cdot b=-4000\cos ((\pi)/(4))`
`[\because \cos (\pi-\theta)=-\cos \theta]`

`a\cdot b=-4000(1)/(√(2))`

`a\cdot b=-(4000)/(√(2))`

Rationalize the above equation.

`a\cdot b=-(4000)/(√(2))* (√(2))/(√(2))`

`a\cdot b=-(4000√(2))/(2)`

`a\cdot b=-2000√(2)`

Therefore, the value of a · b is
`a\cdot b=-2000√(2)`.