Find the values of n, if the points (n + 1, 2n), (3n, 2n + 3) and (5n + 1,5n) are collinear. Find the value of k that the four points (4,1,2), (5, k, 6), (5,1,-1) and (7,4,0) are coplanar. 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. 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).

Find the values of n, if the points (n + 1, 2n), (3n, 2n + 3) and (5n + 1,5n) are collinear. Find the value of k that the four points (4,1,2), (5, k, 6), (5,1,-1) and (7,4,0) are coplanar. 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. 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

Chapter5: Inner Product Spaces

Section5.1: Length And Dot Product In R^n

Problem 81E

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