Question

Hi, we just started vectors in maths class and I don't understand a thing!

Could someone please explain:
Addition of 3 vectors coordinates
Example:
z = (-5, -8)
u = (-2, -6)
w = (-3, -6)
z+u+w = ???

v = (6, 4)
Also, the question says: prove algebraically that vectors v and w have the same direction but different magnitudes

Answer 1

A vector is a direction. If all these vectors are with respect to the origin (0,0) then you simply have to plot the points, and connect the line.
I used the v from your expression (it's obviously not int he same direction as your w, because it is wrong)

Answer 2

to add vectors, you need to add teh components, (x with x, y with y)
z + w + u = (-5,-8) + (-3, -6) + (-2, -6) = (-5 + -3 + -2, -8 + -6 + -6) = (-10, -20)=v

Answer 3

A vector is usually written with coordinates, <x,y> how much it moves in the x direction, how much it moves in the y direction.
w= <-3,-6> for every 3 it moves left, it moves 6 down.
v= <-10,-20> for every 10 it moves left, it moves 20 down.
Notice how w = 3* <-1,-2> and v = 10*<-1,-2>
They have the same vectors! Only different multipliers or magnitude.

Answer 4

Thanks so much could you also help me with this:
w x ( v + z)
w = -3, -2
v = 6, 4
z = -5, -8
In the answer book it says 5 but I didn't get that answer

Answer 5

Oh yeah the x up there is meant to signify multiplication.

Answer 6

when multiplying, you follow a similar concept. <x1,y1> * <x2, y2> = <x1 *x2, y1 * y2>
you have to multiply the x with the x and the y with the y

Answer 7

I did that but did not get the final answer "5"

Answer 8

oh that's not an x, that's a cross. A cross product is the magnitude of the two vectors multiplied by sin ( theta) where theta is the angle between the two vectors.