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ProPatto16
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Homework Statement
Let P be a point not on a plane that passes through points Q, R, S. show that the distance, d, from P to the plane is:
d = |a.(b x c)| over |a x b| where a=QR, b=QS and c=QP
Homework Equations
definition of dot product is a.b=|a||b|cos(theta)
definition of cross product is a x b= |a||b|sin(theta)
triple scalar product is |a.(b x c)|=|b x c||a|cos(theta)
The Attempt at a Solution
putting point P above point S in plane, gives d = |PS| =|PQ|sin(theta) = |c|sin(theta)
theta is angle between |QP| and |QS| which is c and b so by definition of the cross product sin(theta)=|a x b| over |a||b| gives d = csin(theta) = |c||b x c| over |c||b| = |b x c| over |b|
to incorporate dot product i need a cos theta and the only relavant one i can figure is angle between QR and QS which is a and b. which wouldn't be in the plane. I am not sure where to go from here??
thanks