Harder Vector Questions 2

Questions involving vector proofs, finding an unknown ratio or proportion given that points lie on a straight line.

[Sebastian]

Essentially:
Find two different STRAIGHT lines that hit the point "X." They should both have the same scale factor, usually given as the variable, 'k.'
TIP: (Make sure to apply the same rules when determining a straight line, e.g given a line 'ABC, ' find the line segment AB, then AC.)

find the equivalent vector equations of the two straight lines, where using another variable may be needed --- this sets up a simultaneous equation

TIP: (Generally, you'll have to find a portion of one straight line, line segment AB for example in the first tip. You'll then to find another vector equation equivalent to line segment AB. Try and see if you can form one by going on a different line [look at a point, which is a midpoint to line CD or a point that has a ratio {e.g point F located 2:3 on line CD} that somehow attaches itself to point 'X.']

TIP: (think about the two lines as two linear graphs hitting the point 'X, ' easier to understand when applying the skills for simultaneous equations)

Match common factors in directions (put the direction 'a' as an equation, same for direction 'b') e.g
4a - 6ak + 2bk = -4bx - ax

turns to:

a /// 4 - 6k = -x
b /// 2k = -4x

Solve for k.

Finally, read the question: is it asking for:

A ratio of portion (of the line) : full (line)?
(e.g line ABC where AB = kAC)
k can be a whole number or a fraction, depending on the ratio. [portion:full] or [full:portion]

OR

A ratio of [bigger/smaller] partial (of the line) : [bigger/smaller] partial (of the line)?
(e.g line ABC where AB = kBC)
k can be a whole number or a fraction, depending on the ratio. [big:small] or [small:big]

Hope this helped clear things a bit, if you're struggling. Goodluck for the paper 2 on Monday (if your doing last min revision like me lmao)

[tabascodaniel]

thanks for making this! there aren't too many examples of this type of vector question available anywhere else except past papers, so it was very helpful, very much appreciated :)

[Zxrlorn]

Thanks, I understand practically everything now and I'm feeling ready for the exam tomorrow.

[maximusekon]

goat is single handedly saving my gcse maths rn

[richardlau]

Thank you. Very clear explanation of how to set up simultaneous equations and equating coefficients to solve for 'k'. I was stuck on how to set this up before viewing your harder vector videos!

[paulinewanguiobaga]

thank you so much I have been stressing about vectors very badly! this was so much helpful.

[coolguy]

These are some mad questions... pretty sure you don’t even get taught this stuff in class

[michaelswahla]

basically all you do is

find 2 alternative path ways on straight lines to the vector

compare coefficients

find the values of both coefficients

boom

[primsiren]

im so confused as to how you know which vectors to make equal each other. In the parallelogram question you do AX = AX but why cant you do AX = AM like you do on some other questions like the one after?

[markbaird]

You have a great way of explaining things. I wish you did some higher level stuff to cover uni level. Was looking for equation of a plane at the moment but missing being able to use you videos when I moved to uni level engineering maths.

[ramoplayzreal]

21:06 I find it far more simple to make both of the equations equal a value of x, like 36/15(x)=4k & 36/15(x)=6. so that is 4k=6, k=3/2.

[johnpenn]

the way i lost 5 billion braincells while watching this

[comradearno]

The last one i got 3/4 too but in a complete different way...

[fuckthegamecallmonsterlege]

Wait why find AX when you have to find constant for PD?

[jojohn]

I like when you got almost to the end of the last question, you went “what was the question”??

[lsi]

u sure this isnt A level Further math vectors? ☠ cus aint no WAY

[rKaraa]

we get taught this stuff in a level maths not gcse wtff

[hussainfawzer]

These questions are not at all difficult..
Too easy