. Find the volume of the parallelepiped determined by the vectors a = i + j, b = j + k, and c=i+j+k 6. Given that P(3,0,1),Q(−1,2,5),R(5,1,−1), and S(0,4,2). Find the volume of the paral- lelepiped with adjacent edges PQ,PR, and PS. 7. Given that P (1, 1, 1), Q(2, 1, 3), and R(3, −1, 1) are vertices of a triangle. (a) Find the area of the triangle determined by the points P, Q, and R. (b) Find a unit vector perpendicular to plane PQR. 8. Leta=i+2j−k,b=−i+j+k,andc=i+k.Whichvectors,ifany,are (a) perpendicular? (b) Parallel? Give reasons for your answers.
. Find the volume of the parallelepiped determined by the vectors a = i + j, b = j + k, and c=i+j+k 6. Given that P(3,0,1),Q(−1,2,5),R(5,1,−1), and S(0,4,2). Find the volume of the paral- lelepiped with adjacent edges PQ,PR, and PS. 7. Given that P (1, 1, 1), Q(2, 1, 3), and R(3, −1, 1) are vertices of a triangle. (a) Find the area of the triangle determined by the points P, Q, and R. (b) Find a unit vector perpendicular to plane PQR. 8. Leta=i+2j−k,b=−i+j+k,andc=i+k.Whichvectors,ifany,are (a) perpendicular? (b) Parallel? Give reasons for your answers.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.4: Relationships: Perpendicular Lines
Problem 27E
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5. Find the volume of the parallelepiped determined by the vectors a = i + j, b = j + k, and c=i+j+k
6. Given that P(3,0,1),Q(−1,2,5),R(5,1,−1), and S(0,4,2). Find the volume of the paral- lelepiped with adjacent edges PQ,PR, and PS.
7. Given that P (1, 1, 1), Q(2, 1, 3), and R(3, −1, 1) are vertices of a triangle. (a) Find the area of the triangle determined by the points P, Q, and R.
(b) Find a unit vector perpendicular to plane PQR.
8. Leta=i+2j−k,b=−i+j+k,andc=i+k.Whichvectors,ifany,are
(a) perpendicular? (b) Parallel?
Give reasons for your answers.
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