maths p3 vectors help!!

[fluffycloud]

heyy!, the exam is coming up really fast and i am really scared for vectors, mostly because i am clueless, so if anyone could do the vectors question of the winter 2010 paper variant 31, it would be really really great!!

 

[captainjohnprice]

take the directional vector of OP as (x y z). then OP.AB (dot product). put the values of x, y and z from the equ. of AB to the obtained equ. find the value of the constant, which comes -1/6 put this in the equ. of AB find out the value of x, y and z. this will give the psition vector, OP.

 

[fluffycloud]

Thanks, but I kinda needed the last part!
Do you have an idea how to do that?

 

[crash250]

ok guys...but what about part iii for finding the plane...my question is how to find the NORMAL OF PLANE OAB??
i found the direction vector of AB but the normal for OAB is hard,,besides wht they mean BY OAB why O at the beginning


thanks alot

 

[captainjohnprice]

directional vector for the plane perpendicular to OAB is OP, as it (OP) is perpendicular OAB but lies on the plane OAB. use the formula b.n=0 (b is any point on AB). u will get an equ. in the form 2x+5y+7z=0. equate this with a.n ( a being either position vectors OA or OB ) and obtain the equ. 2x+5y+7z=26

 

[crash250]

i wanna know the other way... i mean iam using the simultaneous equating way in which both the direction vector of AB and the normal of the plane OAB(b.n=o)
we solve them and we got a=2 and b=5 and c=7 so my question is who he found the normal of plane OAB ?
ur way is correct but iam using this way so plz again any reply

thanks