Answer all parts of this vector calculus problem please (a) True or False: The only time || + || = |||| is when = 0. You must provide anexplanation to get credit! Hint: think geometrically (you can assume both vectors arein R²)(b) A line L passes through the plane x-2y+3z = 3 at the point (1, 2, 2) in a perpendiculardirection to the plane. Find an equation for the line L.(c) Is it ever possible that u 7=ux ? Explain.tollowsstrici order(d) Describe what the linear transformation determined by the matrixA=2[18]does to the square with vertices (0,0), (1,0), (0, 1) and (1,1).(i.e. figure out what it does to each of the vertices, sketch the new vertices, determinehow the area of this new shape compare to the area of the square)

a. True ||v+u||<=||v|+|u||.This fact is known as the triangle inequality

Answered: (a) True or False: The only time ||+||…

(a) True or False: The only time ||+|| = |||| is when = 0. You must provide an explanation to get credit! Hint: think geometrically (you can assume both vectors are in R²)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 2CM: Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check...

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Question

Answer all parts of this vector calculus problem please

(a) True or False: The only time || + || = |||| is when = 0. You must provide an
explanation to get credit! Hint: think geometrically (you can assume both vectors are
in R²)
(b) A line L passes through the plane x-2y+3z = 3 at the point (1, 2, 2) in a perpendicular
direction to the plane. Find an equation for the line L.
(c) Is it ever possible that u 7=ux ? Explain.
tollows
strici order
(d) Describe what the linear transformation determined by the matrix
A=
2
[18]
does to the square with vertices (0,0), (1,0), (0, 1) and (1,1).
(i.e. figure out what it does to each of the vertices, sketch the new vertices, determine
how the area of this new shape compare to the area of the square)

Calculus that deals with differentiation and integration of the vector field in three-dimensional Euclidean space. It deals with quantities that have both magnitude and direction.

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