Vector help

[Storm5015]

Need help with this question please.... Find a non zero vector orthogonal to the plane through the points P (1,0,0) Q(0,2,0) and R (0,0,3) and find the area of triangle PQR

 

[Unknown008]

Find the cross product of any two vectors of PQ, QR or PR to get the orthogonal vector.


For the area, find the length of any two vectors, and the angle between the two vectors (through dot product). Then use

\(\displaystyle \text{Area} = \dfrac12 ab\sin(\hat{c})\)

for the area of the triangle PQR.

 

[DrPhil]

Actually, the magnitude of the cross product (of any two sides expressed as vectors) is \(\displaystyle a\ b\ \sin{\theta}\), so after finding the vector, just calculate half of its magnitude for the Area