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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 ____°.

Respuesta :

WojtekR
[tex]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}||=\sqrt{2^2+5^2}=\sqrt{4+25}=\sqrt{29}\\\\ ||\bold{v_2}||=\sqrt{4^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5\\\\\\ [/tex]

[tex]\cos\Theta=\dfrac{\bold{v_1}\circ\bold{v_2}}{||\bold{v_1}||\cdot||\bold{v_2}||}=\dfrac{-7}{5\cdot\sqrt{29}}\\\\\\ \cos\Theta=-\dfrac{7}{5\sqrt{29}}\quad\implies\quad\Theta=\arccos\left(-\dfrac{7}{5\sqrt{29}}\right)\\\\\\\boxed{\Theta\approx105,1^\circ}[/tex]
mcherr9

Answer:

18

Step-by-step explanation:

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