Respuesta :
Answer:
1. )[tex]\vec {v}.\vec{u}= -11[/tex]
2.) The angle between v and u is 147.52°.
Step-by-step explanation:
Given:
[tex]\vec {v}= ( -2 , 1 )\\\vec {u}= ( 3 , -5 )[/tex]
To Find:
1. [tex]\vec {v}.\vec{u}= ?[/tex]
2.[tex]\theta = ?[/tex]
Solution:
[tex]\vec {v}.\vec{u}[/tex] is scalar product given as,
[tex]\vec {v}.\vec{u}=|\vec {v}||\vec {u}|\cos \theta[/tex]
[tex]|\vec {v}|=|(-2, 1)|=\sqrt{(-2)^{2} +1^{2}}=\sqrt{5}\\|\vec {u}|=|(3, 5)|=\sqrt{(3)^{2} +(-5)^{2}}=\sqrt{34}[/tex]
[tex]\vec {v}.\vec{u}=(-2i +j).(3i-5j)\\[/tex]
Here only i.i = j.j =1 and i.j = j.i = 0
∴ [tex]\vec {v}.\vec{u}=(-2\times 3 +1\times -5)\\\vec {v}.\vec{u}=-6-5=-11 \\[/tex]
Now, Substituting the above values we get
[tex]-11=\sqrt{5}\times \sqrt{34}\cos \theta\\ \cos \theta=\frac{-11}{\sqrt{170}} \\ \cos \theta =-0.84366\\\therefore \theta =cos^{-1}(-0.84366)\\\therefore \theta =147.52\°[/tex]
As it is negative mean [tex]\theta[/tex] is in Second Quadrant Because Cosine is negative in Second Quadrant.
1. )[tex]\vec {v}.\vec{u}= -11[/tex]
2.) The angle between v and u is 147.52°.
