# Thread: vectors, normal to the plane

1. ## vectors, normal to the plane

Find the normal vector to the plane which is
a) parallel to 4i-2j+2k and i+3j+3k

b) passes through the points O(0,0,0), P(1,-1,2) and Q(3,2,-1)

These are two seperate questions,

for a) i tried using the cross product for the two vectors seperately with a variable of n(xi + yj +zk) and trying to solve the two equations simultaeneously but i realise we have no constants in the equations! I don't know how to tackle the second. Please help i dont understand vectors.

p.s. my maths exam is tomorrow and then i will (try and) never bother you guys again! I am not going to do maths at uni thank the lord.

2. Originally Posted by mathshelpneeded
Find the normal vector to the plane which is
a) parallel to 4i-2j+2k and i+3j+3k
Hello,

you are only asked to calculate the direction of the plane not the equation of a specific plane. Therefore your method is OK. You should have got:
n = -12i + -10j + 14k

Originally Posted by mathshelpneeded
b) passes through the points O(0,0,0), P(1,-1,2) and Q(3,2,-1)
The plane runs through the point O and the vectors OP and OQ define the plane:

p = (0i + 0j + 0k) + r(i - j - 2k) + s(3i + 2j -k), r,s in IR

If you want to use the normal vector (-3, 7, 5) then the equation of the plane becomes:
-3x + 7y + 5z = 0