Question 2 Consider the point P(-2, 1, 4) and the vectors a =< 2,-1,2 > and b=< 3, -2,-2 >. (a) Find the unit vector u that has the opposite direction of a. (b) Find the Plane that passes through the point P and is orthogonal to the vector 6u - 2b. (c) Find the point, if any, at which the Line with parametric equations x=-1-t, y=2+t, z = -3t intersects the Plane found in part b).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question 2
Consider the point
P(-2, 1, 4) and the vectors a =< 2,-1,2 > and
b=<3, -2,-2 >.
(a) Find the unit vector u that has the opposite
direction of a.
(b) Find the Plane that passes through the point P
and is orthogonal to the vector 6u - 26.
(c) Find the point, if any, at which the Line with
parametric equations
x=-1-t, y=2+t, z = -3t
intersects the Plane found in part b).
Transcribed Image Text:Question 2 Consider the point P(-2, 1, 4) and the vectors a =< 2,-1,2 > and b=<3, -2,-2 >. (a) Find the unit vector u that has the opposite direction of a. (b) Find the Plane that passes through the point P and is orthogonal to the vector 6u - 26. (c) Find the point, if any, at which the Line with parametric equations x=-1-t, y=2+t, z = -3t intersects the Plane found in part b).
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