Consider the points below. P(−1, 3, 1), Q(0, 7, 2), R(4, 2, −1) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. <−1,−5,21> (b) Find the area of the triangle PQR.

(a)Therefore the nonzero vector orthogonal to the plane through the points P,Q and R is

(b)Therefore the area of the triangle is square units.

Step-by-step explanation:(

(a)

Given points are P(-1,3,1) , Q(0,7,2) and R(4,2,-1)

The orthogonal vector is

Therefore the nonzero vector orthogonal to the plane through the points P,Q and R is

(b)

The area of the triangle with the vertices P,Q and R is the half of the length of the cross product of and .

          square units.

Therefore the area of the triangle is square units.