Competition - post a photo you've taken of nature >>

Vectors question

The roof of a house has a rectangular base of side four metres by eight metres. The ridge line of the roof is six metres long and one metre above the base of the roof. Calculate the acute angle between two opposite slanting edges of the roof.

How would I visualise this info? I don't know what the roof looks like and which sides go where.

Reply 1

stopopups

Think of it as like a pyramid

Reply 2

TSRforum

Original post by stopopups

Think of it as like a pyramid

What does it mean by '1 metre above the base of the roof'?

Reply 3

TLDM

Not sure about the angle, but I'm fairly sure that's the roof shape they mean.

E: actually, I think I have the wrong angle. But hopefully the rest of it makes sense.
E2: Okay, what actually are they talking about? That last sentence is really vague...

(edited 8 years ago)

Reply 4

TSRforum

How would I display that using three dimensional vectors?

Reply 5

drandy76

Original post by TSRforum

How would I display that using three dimensional vectors?

take on corner point to be the origin, then from there, each other point can be taken as 3d vectors relative to the origin

Reply 6

TSRforum

Original post by drandy76

take on corner point to be the origin, then from there, each other point can be taken as 3d vectors relative to the origin

So I got A = (0,0,0), B= (4,0,0), C= (4,8,0), D= (0,8,0) and V= (2,2,1) thought when I use dot product I still get the wrong answer.

Reply 7

drandy76

Original post by TSRforum

So I got A = (0,0,0), B= (4,0,0), C= (4,8,0), D= (0,8,0) and V= (2,2,1) thought when I use dot product I still get the wrong answer.

would you mind posting your working out?

Reply 8

Alexion

Original post by TSRforum

So I got A = (0,0,0), B= (4,0,0), C= (4,8,0), D= (0,8,0) and V= (2,2,1) thought when I use dot product I still get the wrong answer.

I think your last co-ordinate should be (2,1,1)

Reply 9

TSRforum

Original post by Alexion

I think your last co-ordinate should be (2,1,1)

Tried that one now and still got wrong answer.
I made sure both vectors were directed away from the intersection. I did dot product rule with (2,1,1) and (6,1,1)

Reply 10

Alexion

Original post by TSRforum

Tried that one now and still got wrong answer.
I made sure both vectors were directed away from the intersection. I did dot product rule with (2,1,1) and (6,1,1)

You're mixing your co-ordinates up now (it would be [2,1,1] and [2,7,1]), but I'm not sure what exactly you're trying to do...

Reply 11

drandy76

to be clear, are you using theta = cos-1 dot product/product of magnitude

Reply 12

TSRforum

Original post by drandy76

to be clear, are you using theta = cos-1 dot product/product of magnitude

Yes

Reply 13

TSRforum

Original post by Alexion

You're mixing your co-ordinates up now (it would be [2,1,1] and [2,7,1]), but I'm not sure what exactly you're trying to do...

How did you get 2,7,1? Did you do V-B? If you did C-V what angle does that work out?

(edited 8 years ago)

Reply 14

Alexion

Original post by TSRforum

How did you get 2,7,1? Did you do V-B?

I'm just saying that by defining your corners as XYZ (0,0,0), (4,0,0), (4,8,0) and (0,8,0) you can't have a position with XY (6,2) as that's not above the roof :/

Reply 15

TSRforum

Original post by Alexion

I'm just saying that by defining your corners as XYZ (0,0,0), (4,0,0), (4,8,0) and (0,8,0) you can't have a position with XY (6,2) as that's not above the roof :/