Question

Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = sqrt(2)j, w = 4i

Answer 1

Huh? Some kind of complex vector space?

Answer 2

Sorry i hat , j hat, I get it.

Answer 3

its about parallel and orthogonal vectors. u are supposed to use the dot product (v*w) to see whether the vectors are parallel, orthogonal, or neither

Answer 4

Right, where j is the unit vector in the y-direction and i the unit vector in the x-direction.
Can you write the components of your vectors in standard notation?

Answer 5

I'll do it. In R2 it would be
<0, sqrt(2)> and <4, 0>

Answer 6

so that means the vectors are on the x and y axis meaning they are orthogonal right? because theta=90 degrees

Answer 7

Right, and just to prove it we can do the dot product. It'll make it easier when they aren't like this.

Answer 8

The dot product of w and v is computed by multiplying together their x-components, then their y-components and adding the results together. The result is a scalar not a vector. OK?

Answer 9

ok. thnks so much! I really appreciate ur help!

Answer 10

Can I tell you one more thing?

Answer 11

ok

Answer 12

For any two orthogonal vectors the dot product is 0. That includes R3.
So like, <1,1,1> is perpendicular to <-1,-1,2> because the dot product is 0.
That's spectacular and very useful.