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7) Given the line L:7=(2t+4, 5-3t, t) and the point Q(5,1,-2). (a) Suppose a plane P contains L and Q. Find a normal vector for the plane P. Explain your work carefully and draw a representative picture to illustrate your work.

7) Given the line L:7=(2t+4, 5-3t, t) and the point Q(5,1,-2). (a) Suppose a plane P contains L and Q. Find a normal vector for the plane P. Explain your work carefully and draw a representative picture to illustrate your work.

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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7) Given the line L: F = (21+4, 5-3t, t) and the point Q(5,1,-2). (a) Suppose a plane P contains L and Q. Find a normal vector for the plane P. Explain your work carefully and draw a representative picture to illustrate your work. (b) Find an equation, in standard form, for the plane P, by using what you found in part (a). (c) Write down a point R that is not on the plane P. The coordinates of this point must be nonzero and one of the coordinates must be the number of letters in your first name. Explain how you know the point R you wrote down is not on the plane. (d) Calculate the distance from your point R to the plane P. 4
Transcribed Image Text:7) Given the line L: F = (21+4, 5-3t, t) and the point Q(5,1,-2). (a) Suppose a plane P contains L and Q. Find a normal vector for the plane P. Explain your work carefully and draw a representative picture to illustrate your work. (b) Find an equation, in standard form, for the plane P, by using what you found in part (a). (c) Write down a point R that is not on the plane P. The coordinates of this point must be nonzero and one of the coordinates must be the number of letters in your first name. Explain how you know the point R you wrote down is not on the plane. (d) Calculate the distance from your point R to the plane P. 4
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