Question

Find a.b. IaI =3, IbI = 5 the angle between a and b is 2π/3

Answer 1

Answer:
`a\cdot b= -7.5`

Explanation:

Formula : If a and b be any two vector , then the dot product of and b is given by
`a\cdot b= |a||b|\cos {\theta}` , where
`\theta` is the angle between them.

As per given , we have

IaI =3, IbI = 5
`\theta =(2\pi)/(3)`

Then,
`a\cdot b= (3)(5)\cos (2\pi)/(3)`

`a\cdot b= (15)\cos ( \pi-(\pi)/(3))`

`a\cdot b= (15)(-\cos (\pi)/(3))` (∵ cos (π-x)=-cos x)

`a\cdot b= (15)(-(1)/(2))` [∵
`\cos (\pi)/(3)=(1)/(2)` ]

`a\cdot b= -7.5`

Therefore ,
`a\cdot b= -7.5`