The vector called the ?position vector points from the origin (0, 0, 0) to an arbitrary point in space with coordinates (?x?, ?y?, z?). Use what you know about vectors to prove the following: All points (?x?, ?y?, ?z?) that satisfy the equation ?Ax + ?By + ?Cz = 0, where ?A?, ?B?, and ?C are constants, lie in a plane that passes through the origin and that is perpendicular to the vector . Sketch this vector and the plane.
Solution 102CP Step 1: Given Position vector r = xi + yj + zk ˆ r starts from (0,0,0) and ends at (x,y,z) Step 2: ˆ ˆ ˆ Consider a vector S = Ai + Bj + Ck