Find a vector orthogonal to the plane through the points P, Q, and R and find the area of the triangle PQR.
P(1,0,0) Q(0,2,0) R(0,0,3)© BrainMass Inc. brainmass.com December 24, 2021, 7:34 pm ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
To find a vector orthogonal to the plane, first find any two direction vectors in the plane, then take their cross product:
The vector PQ is Q-P=(-1,2,0)
The vector PR is R-P=(-1,0,3)
The cross product of these is orthogonal to each vector, and therefore to the plane in which they lie.
The area of a triangle with sides given by the vectors a, b and a+b is given by the formula |axb|/2. Applying this formula, using the cross product we already worked out, we see that the area of the triangle PQR is |(6,3,2)|/2=7/2.© BrainMass Inc. brainmass.com December 24, 2021, 7:34 pm ad1c9bdddf>