Consider the point P(-2, 1, 4) and the vectors Question 2 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, intersects the Plane found in part b). z = -3t

Elementary Linear Algebra (MindTap Course List)
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Chapter5: Inner Product Spaces
Section5.1: Length And Dot Product In R^n
Problem 17E: Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of...
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Consider the point P(-2, 1, 4) and the vectors
Question 2
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).
Transcribed Image Text:Consider the point P(-2, 1, 4) and the vectors Question 2 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).
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