Question

If the angle between a bar and bieber is pi by 3 then angle between 2 and minus 3 b is

Answer 1

you mean, angle between $\bar{a}$ and $\bar{b}$ is π/3 then we have to find angle between $2\bar{a}$ and $-3\bar{b}$

use dot product concepts ,

we know, if A and B are two vectors and angle between them is $\theta$

then, $A.B=|A||B|cos\theta$

or, $\theta=cos^{-1}\left(\frac{A.B}{|A||B|}\right)$

case 1 :- $\frac{\pi}{3}=cos^{-1}\frac{\bar{a}.\bar{b}}{|a||b|}$ ........(1)

case 2 : Let angle between $2\bar{a}$ and $-3\bar{b}$ is $\theta$

then, $\theta=cos^{-1}\frac{2\bar{a}.-3\bar{b}}{|2a||-3b|}$

=$cos^{-1}\frac{-6\bar{a}.\bar{b}}{6|a||b|}$

=$\pi-cos^{-1}(1)\frac{\bar{a}.\bar{b}}{|a||b|}$

from equation (1),

= π - π/3 = 2π/3

hence, answer is 2π/3

Answer 2

Answer:

2π/3

Step-by-step explanation:

it is easy you should try and try untile you sucess knowledge and experience will be able and try untile you sucess