Vectors : Conditions for lines to be parallel : ExamSolutions

Tutorial on vectors and the conditions needed for them to be parallel.

[daherabdallah]

For those who are confused you can just make a ratio including b just like we did with a. for example (a-1)/2a=b/15. we can then substitute a with the two value we got earlier, make b the subject of the formula and we'll now have two values for b.
not pretending to be a smart ass but just trying to give another clear method that anyone would want to use instead of the (also correct) way used in this great video. As always great work thanks for being so helpful!

[Kalia_]

From reading the other comments on this video I understand that at the start of the problem, when you're comparing the i components, you make 2a proportional to a-1, i.e. 2a=k(a-1) My question is - why does it have to be that way round? For example, why couldn't you make the proportion (a-1)=k(2a) as isn't it exactly the same? Finally, do you have any videos on "ratio equations, " it completely threw me when you first brought it up as I must have watched hundreds of your videos and yet I've never heard of the term or method before. Thanks!

[TheGuitaristOfGod]

I went ahead and solve the problem a different way and got two extra solutions that seems to work out. Mind telling me if it's good?

Firstly, we know that a variable (x) multiplied by the first vector (l1) must equal the second vector(l2). If you look at the b variable you can see that x*b=15. There are 4 possibilities this could happen:
1)x=1 b=15
2)x=-1 b=-15
3)x=3 b=5
4)x=5 b=3

Replacing each one to get a I got(among the ones you got): a=5/3 b=3 and a=3 b=5

[TheGuitaristOfGod]

Basically, this is what I had in mind the whole time when solving the exercise:
"something times the first direction vector must equal the second direction vector)" or

x (a-1, -a-1, b) = (2a, 3-5a, 15)

There are only four possible ways for x*b to equal 15 (check previous reply). I've taken each x and multiplied to find 'a' (ex. for x=3: 3(a-1) = 2a => a=3) and then replaced a, x, b to see if it checks out (ex. for x=3 and a=3: 3(3-1) = 2*3 => True)

[TheGuitaristOfGod]

By the first vector I mean the direction vector with the lambda in front of it. At 1:20 you said that I should be able to multiply the vector by some value(in my example x) to get the second vector (in my example l2 which is the vector in front of mu)

[ibrahimshafi]

I think this is further, spent 30 mins watching videos that I didn't even know I need

[purplefire]

what if you had two lines, and the direction vectors are not scalar multiples of one another but are exactly the same, can you assume that both lines coincide, or do you still have to check finding the values of lambda mew? thnx for your help!

[GladwinNewton]

So you mean that the directional ratio should be proportional for two vectors to be parallel?

[Cyno]

i'm confused as to why you have lambda and mu in the original vectors. if we added beta in order to find the scale factor, knowing that there should be one because their parallel, why did we need mu and

[xDJxGLDNx]

To get the values of b can you not sub the two values of a into (a-1)/(2a) = b/15?

[gishamolmathew]

Hello,
Thank you for this video...it was extremely useful.
In the introduction at the beginning of the video, you drew onto a diagram (3, -1, 5) and also (2, -3, 1). Are these random or representative of where they actually are?

Thank you very much!

[paisenbob]

I absolutely love these types of questions!

[ExamSolutions_Maths]

and what do you mean by my first vector?

[RShahProductions]

F*ck. I understood exactly why he took (a-1)/(2a) = (-a-1)/(3-5a) but not the stuff before 3:30, now what you've said has helped improve my general understanding of ratios and why multiplying by k works.
Thank you.

[ClayDooH]

anybody else here the dripping and the toilet acoustics? SID making a video whilst taking a poo what a hero

[ExamSolutions_Maths]

Sorry, but I am confused and believe you are wrong. What is your x?

[ExamSolutions_Maths]

random. It does not alter the solution.

[ExamSolutions_Maths]

You cannot assume that they are the same line.

[zamanraja]

Why can’t u say b=15 if u are saying that they are equal ??