Finding the Nonzero Vector and Area of Triangle

[Physicsnoob90]

Homework Statement

Find a nonzero vector orthogonal to the plane through the point P, Q,and R. (b) also find the area of triangle PQR

P(1,0,1) , Q(-2,1,3) , R(4,2,5)

Homework Equations

-Cross product
-Finding the Angle
-Area formula

The Attempt at a Solution

My steps:
1. i found the vectors for PQ = <-3,1,2> and PR = <3,2,4>

2. i perform the cross product (PQ X PR), which got me <0,18,-9>

Can anyone help me?

 

[Physicsnoob90]

NVM, i just solved it!

 

[HallsofIvy]

It is a basic property of the cross product that the length of the cross product of vectors u and v is the area of the parallelogram having vectors u and v as to adjacent sides and so 1/2 the length of their cross product is the area of the triangle having u and v as sides.