4) With respect to the origin 0, the points A and B have position vectors given by OA = i+ 2j + 2k and OB = 3i + 4j a) Find a vector equation for the line AB b) State whether or not the point (4, 2,-2) lies on this line c) Find the acute angle between AB and the line with vector equation r = 3i – j+ 4k + µ(i + 2j – 3k).

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.4: Vectors In Three Dimensions
Problem 2E
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4) With respect to the origin 0, the points A and B have position vectors given by
OA = i + 2j + 2k and OB = 3i + 4j
a) Find a vector equation for the line AE
b) State whether or not the point (4, 2, -2) lies on this line
c) Find the acute angle between AB and the line with vector equation r = 3i –j+4k+µ(i+ 2j – 3k).
Transcribed Image Text:4) With respect to the origin 0, the points A and B have position vectors given by OA = i + 2j + 2k and OB = 3i + 4j a) Find a vector equation for the line AE b) State whether or not the point (4, 2, -2) lies on this line c) Find the acute angle between AB and the line with vector equation r = 3i –j+4k+µ(i+ 2j – 3k).
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