?Let P be a point not on the plane that passes through the points Q, R, and S.(a) Show
Chapter 12, Problem 46(choose chapter or problem)
Let P be a point not on the plane that passes through the points Q, R, and S.
(a) Show that the distance d from P to the plane is
\(d=\frac{|a \cdot(b \times c)|}{|a \times b|}\)
Where \(a=\overrightarrow{Q R}\) ,\(b=\overrightarrow{Q S}\) and \(c=\overrightarrow{Q P}\)
(b) Use the formula in part (a) to find the distance from the point \(P(2, 1, 4)\) to the plane through the points \(Q(1, 0, 0), R(0, 2, 0)\), and \(S(0, 0, 3)\).
Equation Transcription:
P(2, 1, 4)
Q(1, 0, 0)
R(0, 2, 0)
S(0, 0, 3)
Text Transcription:
d=|a times (b times c)|/|a times b|
a=^rightarrow QR
b=^rightarrow QS
b=^rightarrow QP
P(2, 1, 4)
Q(1, 0, 0)
R(0, 2, 0)
S(0, 0, 3)
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