1. Given the points O (0, 0, 0), P (2, 6, −1), Q (1, 1, 1) and R (4, 6, 2), find a vector that is perpendicular to both
(a) OP and OQ (b) PQ and QR (c) RP and QR
2. Find an equation of the plane passing through point P and having vector n as a normal.
P (−1, 3, −2); n = (-2,1,-1)
3. Find an equation of the plane that passes through the given points.
P (5, 4, 3), Q (4, 3, 1), R (1, 5, 4)
I'm thankful for the reply but i still dont understand part 2 and 3 solution, could u explain it in a simpler manner?
as in what does vector p is stationary vector of P and
why is there a vector n beside it?
for part 3;
i totally got no idea what it means
with the equation..i know nothing about it.
so sorry, could u explain more specifically?
thanks and sorry for the troubles.
is the given normal vector of the plane; describes any vector which is placed in the plane and therefore the dotproduct of these 2 vectors must be zero. Thus you get:
Multiply the brackets:
for part 3;
i totally got no idea what it means
with the equation..i know nothing about it. <<<<<<<< what exactly have you done in vector geometry so far?
so sorry, could u explain more specifically?
thanks and sorry for the troubles.Two points define a vector (and of course a straight line), three points define a plane. To determine a plane you need one fixed point P and two different directions (exactly: non-collinear). Then any point of the plane (which has the coordinates (x, y, z)) is described by:3. The plane has the equation: