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

Answer:

$a\cdot b=-2000\sqrt{2}$

Step-by-step 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.

$a\cdot b=(80)(50)\cos (\frac{3\pi}{4})$

$a\cdot b=4000\cos (\pi-\frac{\pi}{4})$

$a\cdot b=-4000\cos (\frac{\pi}{4})$           $[\because \cos (\pi-\theta)=-\cos \theta]$

$a\cdot b=-4000\frac{1}{\sqrt{2}}$

$a\cdot b=-\frac{4000}{\sqrt{2}}$

Rationalize the above equation.

$a\cdot b=-\frac{4000}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

$a\cdot b=-\frac{4000\sqrt{2}}{2}$

$a\cdot b=-2000\sqrt{2}$

Therefore, the value of a · b is $a\cdot b=-2000\sqrt{2}$.