Finding the Nonzero Vector and Area of Triangle

  • #1

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?
 

Answers and Replies

  • #3
HallsofIvy
Science Advisor
Homework Helper
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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.
 

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