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4. Find an equation (in point-normal form) of the plane containing the points K, M, and N. 5. Let R be the parallelogram having line segments KM and MN as adjacent sides. Show that R is a rectangle. 6. Determine if the vector KM and the line & are parallel.

4. Find an equation (in point-normal form) of the plane containing the points K, M, and N. 5. Let R be the parallelogram having line segments KM and MN as adjacent sides. Show that R is a rectangle. 6. Determine if the vector KM and the line & are parallel.

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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Consider the points K(-1,0, 7) and M(1, -2,5), the vector MN = (1,4, -3), and the line with symmetric cquations 16x=y-18= z +11. 1. Determine the coordinates of point N. 2. Write the vector KM in terms of its components. 3. Find the equation (in center-radius form) of the sphere having KM as a diameter. 4. Find an equation (in point-normal form) of the plane containing the points K, M, and N. 5. Let R be the parallelogram having line segments KM and MN as adjacent sides. Show that R is a rectangle. 6. Determine if the vector KM and the line are parallel.
Transcribed Image Text:Consider the points K(-1,0, 7) and M(1, -2,5), the vector MN = (1,4, -3), and the line with symmetric cquations 16x=y-18= z +11. 1. Determine the coordinates of point N. 2. Write the vector KM in terms of its components. 3. Find the equation (in center-radius form) of the sphere having KM as a diameter. 4. Find an equation (in point-normal form) of the plane containing the points K, M, and N. 5. Let R be the parallelogram having line segments KM and MN as adjacent sides. Show that R is a rectangle. 6. Determine if the vector KM and the line are parallel.
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