Answer: [tex]a\cdot b= -7.5[/tex]
Step-by-step explanation:
Formula : If a and b be any two vector , then the dot product of and b is given by [tex]a\cdot b= |a||b|\cos {\theta}[/tex] , where [tex]\theta[/tex] is the angle between them.
As per given , we have
IaI =3, IbI = 5 [tex]\theta =\dfrac{2\pi}{3}[/tex]
Then, [tex]a\cdot b= (3)(5)\cos \dfrac{2\pi}{3}[/tex]
[tex]a\cdot b= (15)\cos ( \pi-\dfrac{\pi}{3})[/tex]
[tex]a\cdot b= (15)(-\cos \dfrac{\pi}{3})[/tex] (∵ cos (π-x)=-cos x)
[tex]a\cdot b= (15)(-\dfrac{1}{2})[/tex] [∵[tex]\cos \dfrac{\pi}{3}=\dfrac{1}{2}[/tex] ]
[tex]a\cdot b= -7.5[/tex]
Therefore , [tex]a\cdot b= -7.5[/tex]
