(708,#23) A) Find the vector orthogonal to the plane through the points

(708,#23) a) Find the vector orthogonal to the plane through the points P (0,0,0), Q(1,-1,1), R(4,3,7).
b)Find the area of the triangle PQR.
Solution:

a) Let a and b be the vectors defined below. Then the orthogonal vector is the cross product a x b.

Therefore, the vector orthogonal to the plane is
b) = area of parallelogram formed by vectors a and b.
= area of the triangle formed by vectors a, b and a + b

Therefore, the area of the triangle is .

by:sh