Consider a point Q(x1, y1, z1) and a line L given by the vector equation r = r0 +tv,where r0 = <x0, y0, z0> and v = <a, b, c>. Prove that the distance d from the point Q to the line L isd = |v × <x1 − x0, y1 − y0, z1 − z0>|/|v|.
Consider a point Q(x1, y1, z1) and a line L given by the vector equation r = r0 +tv,where r0 = <x0, y0, z0> and v = <a, b, c>. Prove that the distance d from the point Q to the line L isd = |v × <x1 − x0, y1 − y0, z1 − z0>|/|v|.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 20CM
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Consider a point Q(x1, y1, z1) and a line L given by the
r = r0 +tv,
where r0 = <x0, y0, z0> and v = <a, b, c>. Prove that the distance d from the point Q to the line L is
d = |v × <x1 − x0, y1 − y0, z1 − z0>|/|v|
.
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