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Let P(4, 3, –1) and Q(6, – 1,3) be two points in three-dimensional space. (a) Find the distance between P and Q. (b) Find an equation for the sphere whose center is P and for which the segment PO is a radius of the sphere. (c) The vector u has initial point P and terminal point Q. Express u both in component form and using the vectors i, j, and k.

Let P(4, 3, –1) and Q(6, – 1,3) be two points in three-dimensional space. (a) Find the distance between P and Q. (b) Find an equation for the sphere whose center is P and for which the segment PO is a radius of the sphere. (c) The vector u has initial point P and terminal point Q. Express u both in component form and using the vectors i, j, and k.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let P(4, 3, –1) and Q(6, – 1,3) be two points in three-dimensional space. (a) Find the distance between P and Q. (b) Find an equation for the sphere whose center is P and for which the segment PO is a radius of the sphere. (c) The vector u has initial point P and terminal point Q. Express u both in component form and using the vectors i, j, and k.
Transcribed Image Text:Let P(4, 3, –1) and Q(6, – 1,3) be two points in three-dimensional space. (a) Find the distance between P and Q. (b) Find an equation for the sphere whose center is P and for which the segment PO is a radius of the sphere. (c) The vector u has initial point P and terminal point Q. Express u both in component form and using the vectors i, j, and k.
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