Question

Find the magnitude ||v|| and direction angle θ, to the nearest tenth of a degree, for the given vector v. v = -4i - 3j

B. 7; 216.9°
C. 5; 216.9°
D. 5; 36.9°

Answer 1

@MaimiGirl help with this last one?

Answer 2

do you know what the definition of the magnitude is?

Answer 3

sorry i am blank on this one

Answer 4

No

Answer 5

I'll sit back and learn from @RBauer4

Answer 6

me too :) cause Idk about this

Answer 7

We can define the magnitude as the square root of the sum of the components squared. For example, our vector is this caseis\[\left(\begin{matrix}-4 \\ -3\end{matrix}\right)\]

Answer 8

So the magnitude would be \[\sqrt{ (-4)^2 + (-3)^2}\]

Answer 9

ok what would I do next

Answer 10

To find the azimuthal angle of this vector, we can analyze its scalr product against i. There is an equation, <x , y> = ||x||*||y||cos(theta), where theta is the angle between vectors x and y.

Answer 11

Let x equal our vector and let y be i.

Answer 12

Ok, i am with you

Answer 13

So let's solve for theta.

Answer 14

ok how do you do that i am sorry i don't know how

Answer 15

<x,y> = -4*1 + -3*0 = -4 , ||x|| = 5, ||y|| = 1 so cos(theta) = -4/5

Answer 16

ok i am starting to understand

Answer 17

What was A for this question?

Answer 18

I got it wrong so i didn't post it

Answer 19

but this was A. 5; 233.1°

Answer 20

i see. I ask because our vector points in the third quadrant. So our angle will be greater than 180, but less than 270.

Answer 21

I was thinking C. but i wasn't really sure

Answer 22

C doesn't make since calculations wise. If we were to measure from 180 to theta, then we would get about 36.9.

Answer 23

so it would be 5; 36.9°

Answer 24

I think you might be right
I would go for C, since 360 - 143.1 = 216.9

Answer 25

That was what I was thinking but i wasn't 100% sure