Introduction To Three Dimensional Geometry

Since, points

(a%2C%20b)%2C%20(b%2C%20a)

and

(a%5E2%2C%20-%20b%5E%202)

are collinear.

%5Ctherefore%20%5Cbegin%7Bvmatrix%7Da%26b%261%5C%5C%20b%26a%261%5C%5C%20a%5E%7B2%7D%26-b%5E%7B2%7D%261%5Cend%7Bvmatrix%7D%20%3D%200

Applying,

R_%7B2%7D%20%5Cto%20R_%7B2%7D%20-%20R_%7B1%7D

and

R_%7B3%7D%20%5Cto%20R_%7B3%7D%20-R_%7B1%7D

%5CRightarrow%5Cbegin%7Bvmatrix%7Da%26b%261%5C%5C%20b-a%26a-b%260%5C%5C%20a%5E%7B2%7D-a%26-b%5E%7B2%7D-b%260%5Cend%7Bvmatrix%7D%20%3D%200

%5CRightarrow%5Cbegin%7Bvmatrix%7Db-a%26a-b%5C%5C%20a%5E%7B2%7D-a%26-b%5E%7B2%7D-b%5Cend%7Bvmatrix%7D%20%3D%200

%5CRightarrow%20%5Cleft(a-b%5Cright)%5Cbegin%7Bvmatrix%7D-1%261%5C%5C%20a%5E%7B2%7D-a%26-b%5E%7B2%7D-b%5Cend%7Bvmatrix%7D%20%3D%200

%5CRightarrow%20%5Cleft(a-b%5Cright)%5Cleft(b%5E%7B2%7D%20%2Bb%2Ba%5E%7B2%7D%2Ba%5Cright)%20%3D%200

%5CRightarrow%20%5Cleft(a-b%5Cright)%5Cleft(a%2Bb%5Cright)%5Cleft(b%2B1-a%5Cright)%20%3D0

%5CRightarrow

Either

a%20-%20b%20%3D%200

%5Cleft(a%20%2B%20b%5Cright)%20%3D%200

%5Cleft(b%20%2B%201%20-%20a%5Cright)%20%3D%200

Chapter Questions
1 MCQs