Question

Please help!
Let v=(5,-2) and w=(-10,4). Which of the following are true? Check all that apply.
a. w=-2v
b. the y-component of w is 4.
c. v*w=-58
d. v and w are perpendicular

Answer 1

x y
v = ( 5, -2)
w = (-10, 4).

Answer 2

okay but I still don't understand

Answer 3

ok... well, what.... part? :)

Answer 4

how to find the answer! ahah

Answer 5

I think A is true?

Answer 6

what's the "y" in the vector w?

Answer 7

4

Answer 8

b. the y-component of w is 4.

Answer 9

oh okay! So A and B are true, how about the other ones? How do I multiply v and w together?

Answer 10

now, -2<5, -2> => <(-2*5), (-2*-2)> => <-10, 4> = w

Answer 11

yeah, the multiplication, so-called the dot product

\(\bf <a, b> \cdot <c, d> \implies a\times c + b \times d\)

Answer 12

so 5*-10+-2*4=-58

Answer 13

yeap

Answer 14

so C is also true, do you know if they are perpendicular?

Answer 15

2 vectors are perpendicular, or so-called orthogonal, if their dot product equals 0

Answer 16

Okay so they are not! Thanks so, so much!! :)

Answer 17

yw