Let ū = (0, 1, –1), ū = (1, 1, 0) and w = (2, 1, 1).a) Show that ū, ī and w lie in the same plane when positioned so that their initial pointscoincide.b) Find parametric equations of the plane (P) containing the point A(1,2, – 1) and the vectorsū and ū.c) Find Proj,ū.1d) Find the equation of the plane (Q) passes through the point B(-1,0, 1) and is orthogonal toū x ū.e) Find the distance between the two parallel planes (P) and (Q).f) Calculate the cosine of the angle 0 between ū and ū.

Vectors u ,v and w lie in same plane if u.(vxw) = 0 Here u = (0,1,-1) v = (1,1,0) w= (2,1,1) 3…

Let ū = (0, 1, –1), ū = (1, 1, 0) and w = (2, 1, 1). a) Show that ū, ī and w lie in the same plane when positioned so that their initial points coincide. b) Find parametric equations of the plane (P) containing the point A(1,2, – 1) and the vectors ū and ū. c) Find Proj,ū.

Let ū = (0, 1, –1), ū = (1, 1, 0) and w = (2, 1, 1). a) Show that ū, ī and w lie in the same plane when positioned so that their initial points coincide. b) Find parametric equations of the plane (P) containing the point A(1,2, – 1) and the vectors ū and ū. c) Find Proj,ū.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 47EQ

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Question

Let ū = (0, 1, –1), ū = (1, 1, 0) and w = (2, 1, 1).
a) Show that ū, ī and w lie in the same plane when positioned so that their initial points
coincide.
b) Find parametric equations of the plane (P) containing the point A(1,2, – 1) and the vectors
ū and ū.
c) Find Proj,ū.
1
d) Find the equation of the plane (Q) passes through the point B(-1,0, 1) and is orthogonal to
ū x ū.
e) Find the distance between the two parallel planes (P) and (Q).
f) Calculate the cosine of the angle 0 between ū and ū.

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