Carry out the following steps to determine the (least) distance between the point P and the line

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Carry out the following steps to determine the (least) distance between the point P and the line ℓ through the origin.

a. Find any vector v in the direction of ℓ.

b. Find the position vector u corresponding to P.

c. Find projvu.

d. Show that w = u - projvu is a vector orthogonal to v whose length is the distance between P and the line ℓ.

e. Find w and |w|. Explain why |w| is the least distance between P and ℓ.

P(1, 1, -1); ℓ is parallel to (-6, 8, 3)

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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