Use the determinants to solve the following questions: (a) Find the values of n, if the points (n + 1, 2n), (3n, 2n + 3) and (5n + 1,5n) are collinear. (b) Find the value of k that the four points (4,1,2), (5, k, 6), (5,1,-1) and (7,4,0) are coplanar. (c) Find the value of r if the area of the triangle is formed by the points (-3,6),(4,4) and (r,-2) is 12 sq units. (d) Find the volume of tetrahedron whose vertices are A(1,1,0), B(-4,3,6), C(-1,0,3) and D(2,4,-5).
Use the determinants to solve the following questions: (a) Find the values of n, if the points (n + 1, 2n), (3n, 2n + 3) and (5n + 1,5n) are collinear. (b) Find the value of k that the four points (4,1,2), (5, k, 6), (5,1,-1) and (7,4,0) are coplanar. (c) Find the value of r if the area of the triangle is formed by the points (-3,6),(4,4) and (r,-2) is 12 sq units. (d) Find the volume of tetrahedron whose vertices are A(1,1,0), B(-4,3,6), C(-1,0,3) and D(2,4,-5).
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.CM: Cumulative Review
Problem 25CM: Use a determinant to find an equation of the line passing through the points (1,4) and (5,2)
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Transcribed Image Text:Use the determinants to solve the following questions:
(a) Find the values of n, if the points (n + 1, 2n), (3n, 2n + 3) and (5n + 1,5n) are collinear.
(b) Find the value of k that the four points (4,1,2), (5, k, 6), (5,1,-1) and (7,4,0) are coplanar.
(c) Find the value of r if the area of the triangle is formed by the points (-3,6),(4,4) and (r,-2) is
12 sq units.
(d) Find the volume of tetrahedron whose vertices are A(1,1,0), B(-4,3,6), C(-1,0,3) and
D(2,4,-5).
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