## anonymous one year ago precalc givin medals 1. Let u = <-4, 1>, v = <-1, 6>. Find -2u + 4v. <4, 22> <4, 7> <12, -26> <10, -14> 2. Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <3, 0>, v = <0, -6> Orthogonal Neither Parallel

1. freckles

u is a vector the -2 in front of the vector u is a scale factor it is just a number you multiply to each component of u

2. freckles

from number 2 have you considered finding the dot product?

3. freckles

and the magnitudes of the vectors as well

4. freckles

$\cos(\theta)=\frac{a \cdot b}{|a| \cdot |b|} \\ \theta=\arccos( \frac{ a \cdot b}{|a| \cdot |b|}) \\ \text{ if } \theta=90^o \text{ then } a \text{ and } b \text{ are orthogonal } \\ \text{ but to find out if they are orthogonal you only need to see if } a \cdot b=0 \\ \text{ this is much shorter than actually finding the angle between the two vectors }$ $\text{ if } \theta=0^o \text{ or } \theta=180^o \text{ then you have that } a \text{ and } b \\ \text{ are parallel } \\ \text{ but you don't really need to find } \theta \\ \text{ you could just see if } a \cdot b=|a| \cdot |b| \text{ or if } a \cdot b =-|a| \cdot |b|$

5. anonymous

@freckles orthogonal?

6. dan815

u and v are definately orth as one is completely in x and the onther is in y

7. dan815

|dw:1435093656622:dw|

8. dan815

and the dot product is also 0, <3,0> dot <0,-6>=3*0+0*-6=0

9. anonymous

@dan815 what did u get for #1

10. freckles

1. Let u = <-4, 1>, v = <-1, 6>. Find -2u + 4v. do you know how to find -2u and 4v?

11. dan815

vector addition is done component by component

12. anonymous

no help @dan815 @freckles

13. freckles

hard to help when you don't answer questions like do you know how to find -2u and 4v? I guess you are going to just ignore that question and say we weren't helping you. I don't see how we weren't helping you unless your definition of not help is not getting a direct answer.