(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant 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)

3. 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 wouldnt be in the plane. im not sure where to go from here??

thanks

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# Distance formula for between a point and a plane

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