Question

HELP PLEASE SOON!

1. If v1= (2, 4) and v2= (-1, 5), then v1*v2 is equal to which of the following?
A. 22
B. (8, -5)
C. 18
D. (-2, 20)

I think its either C or D but idk if you are supposed to add the two numbers together which would equal C or not.

2. If v1= (2, 5) and v2= (4, -3), then the angle between the two vectors is ____°.

Answer 1

18

Explanation:

Answer 2

`1.\\\\\bold{v_1}=\langle2,4\rangle\qquad\bold{v_2}=\langle-1,5\rangle\\\\ \bold{v_1}\circ\bold{v_2}=2\cdot(-1)+4\cdot5=-2+20=18\qquad [\text{C}]\\\\\\ 2.\\\\ \bold{v_1}= \langle2, 5\rangle\qquad \bold{v_2}= \langle4, -3\rangle\\\\\\ \bold{v_1}\circ\bold{v_2}=2\cdot4+5\cdot(-3)=8-15=-7\\\\||\bold{v_1}||=√(2^2+5^2)=√(4+25)=√(29)\\\\ ||\bold{v_2}||=√(4^2+(-3)^2)=√(16+9)=√(25)=5\\\\\\`


`\cos\Theta=\frac{\bold{v_1}\circ\bold{v_2}}{||\bold{v_1}||\cdot||\bold{v_2}||}=(-7)/(5\cdot√(29))\\\\\\ \cos\Theta=-(7)/(5√(29))\quad\implies\quad\Theta=\arccos\left(-(7)/(5√(29))\right)\\\\\\\boxed{\Theta\approx105,1^\circ}`