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9. (a) Find the value of b when the angle between v = (b,2) and w = (-8, –6) is -. (b) Find a unit vector perpendicular to the plane through P(2, 1, –1), Q(-1,1, 2) and R(1,–1,2). (c) Find the equation of the plane containing the line x = -1+ t, y = 1- 2t, z =t and is perpendicular to the other two planes 4x- 2y + 2z – 1 = 0 and 3x – 6y + 3z = -5.

9. (a) Find the value of b when the angle between v = (b,2) and w = (-8, –6) is -. (b) Find a unit vector perpendicular to the plane through P(2, 1, –1), Q(-1,1, 2) and R(1,–1,2). (c) Find the equation of the plane containing the line x = -1+ t, y = 1- 2t, z =t and is perpendicular to the other two planes 4x- 2y + 2z – 1 = 0 and 3x – 6y + 3z = -5.

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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9. (a) Find the value of b when the angle between v= (b, 2) and w = (-8, –6) is . (b) Find a unit vector perpendicular to the plane through P(2, 1, –1), Q(-1,1,2) and R(1,–1,2). (c) Find the equation of the plane containing the line x = -1+t, y = 1- 2t, z = t and is perpendicular to the other two planes 4x - 2y + 2z – 1 = 0 and 3x – 6y + 3z = -5.
Transcribed Image Text:9. (a) Find the value of b when the angle between v= (b, 2) and w = (-8, –6) is . (b) Find a unit vector perpendicular to the plane through P(2, 1, –1), Q(-1,1,2) and R(1,–1,2). (c) Find the equation of the plane containing the line x = -1+t, y = 1- 2t, z = t and is perpendicular to the other two planes 4x - 2y + 2z – 1 = 0 and 3x – 6y + 3z = -5.
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