Question 3i part b 3. (i) a) If A is the point (3,5,7) and B is the point (-1,0, 3), compute the vector AB.b) An object located at a point P is moved through the vector (1 2 4). If thefinishing point of the object is (5, -4,3), what are the coordinates of P?c) Find a unit vector with the same direction as (-2 -2 4).(ii) Compute the dot product of the following vectors, and hence compute the anglebetween them: (¹), (√3-1 √3+1).(iii) Find the equation of the plane which is orthogonal to the vector (1,3,-2) andpasses through the point (1, 1,0).(iv) The planes x-y+5z = 1 and 2x+3y-z = 0 intersect in a line. By solving a linearsystem or otherwise, find this line, giving your answer in vector representation.

Answered: Image /qna-images/answer/67508f8d-a816-4978-aa80-77d0d0fc77d5.jpg

b) An object located at a point P is moved through the vector (1 2 4). If the finishing point of the object is (5,-4,3), what are the coordinates of P? c) Find a unit vector with the same direction as (-2 -2 4).

b) An object located at a point P is moved through the vector (1 2 4). If the finishing point of the object is (5,-4,3), what are the coordinates of P? c) Find a unit vector with the same direction as (-2 -2 4).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 13CR

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Question

Question 3i part b

3. (i) a) If A is the point (3,5,7) and B is the point (-1,0, 3), compute the vector AB.
b) An object located at a point P is moved through the vector (1 2 4). If the
finishing point of the object is (5, -4,3), what are the coordinates of P?
c) Find a unit vector with the same direction as (-2 -2 4).
(ii) Compute the dot product of the following vectors, and hence compute the angle
between them: (¹), (√3-1 √3+1).
(iii) Find the equation of the plane which is orthogonal to the vector (1,3,-2) and
passes through the point (1, 1,0).
(iv) The planes x-y+5z = 1 and 2x+3y-z = 0 intersect in a line. By solving a linear
system or otherwise, find this line, giving your answer in vector representation.

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Similar questions

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