Vectors

[ninbam1k]

A, B and C are 2i - j, 5i + j, 7i + 4j.

P is the point with position vector OP = xi + yj + zk

P lies 2 units above the plan containing ABC
P is equidistant from O, A and B

Find x, y, z

[kamil9876]

I'm assuming your first sentence reads: "OA,OB and OC are...". Hence I will assume so.

Since all of those vectors have a component of , the plane must be the plane. Hence we immediately see that . Now just use the equidistance property to set up some simultaenous equations:

(using )



Now using

and now expand like above to get another linear equation which you can solve simultaenously.

Notice: point C was redundant here, so I suspect you probably made a typo but my way is correct given what you have written.

[xZero]

i got some really ugly answer so im not sure if i did it right or not. anyways

since P is 2 units above the plane containing ABC and non of the have the K component, z=2

from here on we can ignore the k component since oabc doesnt have it

for P to be equidistant from O, A and B, the magnitude of OP, AP and BP must equal
so OP = xi + yj
AP = x-2i + y+1j
BP = x-5i + y-1j

then you equate the magnitude of them together and the solution i got was x=31/14 and y=27/14

final answer, x=31/14 y=27/14 and z=2

Edit: ninja'd