Question

Can someone help me with vectors? Will post picture on comments

Answer 1

I'd help you, but that picture is small and sideways.

Answer 2

@inkyvoyd

Answer 3

a. The floor of the attic is along the xy-plane. How far will the peak of the roof be above this floor? How can you tell?

b. How long and how wide will the house be?

Answer 4

Damnit, you caught me. @jim_thompson5910 please help her? Thank you :)

Answer 5

the z component of the vector v is 8

so the peak is 8 ft away from the floor of the attic

Answer 6

the x and y components of the vector h are: 20 and 45

so the width of the house is 20 ft and the length of the house is 45 ft

Answer 7

Okay. I see. It also asks me how long to make the rafter that goes from the corner with the marked angle to the peak of the roof along the slanted ridge. How long will this rafter be? What would i have to do?

Answer 8

@jim_thompson5910 what is the rafter?

Answer 9

find the length of vector v

Answer 10

by doing magnitude?

Answer 11

use the formula

|v| = sqrt(x^2 + y^2 + z^2)

Answer 12

correct

Answer 13

and that would be the rafter?

Answer 14

length of it yes

Answer 15

so what does the angle have to do with it?

Answer 16

not exactly sure, maybe that's for a different problem

Answer 17

it's not asking anything about the angle at the moment

Answer 18

I see. It is asking me about roof tiles that will lie above the rafter and that they will have to be cut at an angle. Is that angle the one shown?

Answer 19

possibly, but I'm having trouble visualizing how they would be placed exactly

Answer 20

in the picture it shows an angle in the corner. would that be it?

Answer 21

I think so, but I'm not 100% sure about that part

Answer 22

if they want that angle though, you first need to find the vector z = v - h

then you find the angle of that vector

Answer 23

angle of vector z?

Answer 24

yes

Answer 25

is there an equation?

Answer 26

I guess if you really want to be technical, you want the angle between the vector z and the vector w

where

w = < 20, 0, 0 >

Answer 27

If you want to find the angle between vectors u and v, then

theta = arccos[ (u dot v)/(|u|*|v|) ]

where

u dot v = dot product of vectors u and v
|u| = length of vector u
|v| = length of vector v

Answer 28

sorry I should make the clarification

the vector w is really w = <-20, 0, 0>

Answer 29

and vector u and v would be w and z?

Answer 30

correct

Answer 31

z would be <-10,-10,8>?

Answer 32

let me double check

Answer 33

I'm getting the same

Answer 34

so yes, z = < -10, -10, 8>

Answer 35

okay i see! thank you!

Answer 36

you're welcome