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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 Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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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.
Transcribed Image Text: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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