If L is a line in 2-space or 3-space that passes through the points A andB, then the distance from a point P to the line L is equal to the lengthof the component of the vector AP that is orthogonal to the vector AB.PABUse the method above to find the distance from the point P(-3, 1, 4)to the line through A(1, 1,0) and B(-2,3, –4).

Introduction: The dot product of two vectors A and B is given by, A→·B→=|A||B|cosθ

Answered: ne distance from a point P nponent of…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 87E

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Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check your work against the answers in the back of the book. Write w=(7,2,4) as a linear combination of the vectors v1, v2 and v3 if possible. v1=(2,1,0), v2=(1,1,0), v3=(0,0,6)
Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of its length. b u has the direction opposite that of v and twice its length.
A vector in three dimensions can be written in either of two forms: in coordinate form as v=a1,a2,a3 and in terms of the _________ vectors i,j, and k as v= __________. The magnitude of the vector v is |v|= _________. So 4,2,4=i+j+k and 7j24k=,,.
Proof When V is spanned by {v1,v2,...,vk} and one of these vector can be written as a linear combination of the other k1 vectors, prove that the span of these k1 vector is also V.

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ne distance from a point P nponent of the vector AP