The Student Room Group

Vector equation of a line. Help!

Hey, so my teacher knows how much I eternally suck at triangles and yet she keeps giving me proofs that involve them. She is sly. I was just wondering if anybody could possibly give me the direction I need to go in order to prove:

|r|sin(theta) = |a|sin(phi)

I've set up the vector line with b as the vector, AR as two position vectors on b and the vectors a and r from the origin, but I don't know what to do from now! Pretty sure it has to do with cosine angles but I can't set up triangles to save my life.
Reply 1
Avatar for BabyMaths
BabyMaths
Original post by tjsmith94
Hey, so my teacher knows how much I eternally suck at triangles and yet she keeps giving me proofs that involve them. She is sly. I was just wondering if anybody could possibly give me the direction I need to go in order to prove:

|r|sin(theta) = |a|sin(phi)

I've set up the vector line with b as the vector, AR as two position vectors on b and the vectors a and r from the origin, but I don't know what to do from now! Pretty sure it has to do with cosine angles but I can't set up triangles to save my life.


:confused:
Reply 2
Avatar for tjsmith94
tjsmith94
OP
9
Original post by BabyMaths
:confused:


I was too! It's not actually on the syllabus but my further maths lecturer likes us to make proofs for equations so we know why we're using them and not just what they are. I've worked it out now, my explanation of the problem wasn't the best (I suck at "using words" for maths) but basically you end up using the sin rule to get (a/sin(theta))=(r/sin(180-(phi))), and sin(180-(phi)) is equal to sin(phi) so a(sin(phi)) = r(sin(theta)). It was long and icky and I hate proving things.
Reply 3
Avatar for aznkid66
aznkid66
1
Original post by tjsmith94
Hey, so my teacher knows how much I eternally suck at triangles and yet she keeps giving me proofs that involve them. She is sly. I was just wondering if anybody could possibly give me the direction I need to go in order to prove:

|r|sin(theta) = |a|sin(phi)

I've set up the vector line with b as the vector, AR as two position vectors on b and the vectors a and r from the origin, but I don't know what to do from now! Pretty sure it has to do with cosine angles but I can't set up triangles to save my life.


Um...We need more information, a diagram, or even better the original statement you want to prove because we have no clue what r, a, theta, and phi are....
Reply 4
Avatar for Chaoslord
Chaoslord
16
Original post by aznkid66
Um...We need more information, a diagram, or even better the original statement you want to prove because we have no clue what r, a, theta, and phi are....


+1
Reply 5
Avatar for tjsmith94
tjsmith94
OP
9
Original post by aznkid66
Um...We need more information, a diagram, or even better the original statement you want to prove because we have no clue what r, a, theta, and phi are....


Yeah, it was a bit rushed sorry. :tongue:

The vector equation of a line is:
(r-a) x b = 0,
or (r x b) = (a x b)

Because of the cross product rule:
|r||b|sin(theta)n = |a||b|sin(phi)n

You can divide both sides by n and |b|, so therefore
|r|sin(theta) = |a|sin(phi)

I just had to prove it - there wasn't a question as such. I guess this would be the closest image:


I've done it now but if you want to have a crack at it be my guest. :biggrin:
vecline.gif7.5KB

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you