Answer :

Given :


Let A, B, C & D be four points with position vectors .


Therefore,






To Prove : Points A, B, C & D are coplanar.


Formulae :


1) Vectors :


If A & B are two points with position vectors ,


Where,




then vector is given by,




2) Scalar Triple Product:


If





Then,



3) Determinant :



Answer :


For given position vectors,






Vectors are given by,




………eq(1)




………eq(2)




………eq(3)


Now, for vectors







= 2(21) – 4(15) + 6(3)


= 42 – 60 + 18


= 0



Hence, vectors are coplanar.


Therefore, points A, B, C & D are coplanar.


Note : Four points A, B, C & D are coplanar if and only if


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

The angle betweenMathematics - Exemplar

True and False<brMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Fill in the blankMathematics - Exemplar

True and False<brMathematics - Exemplar

True and False<brMathematics - Exemplar

Fill in the blankMathematics - Exemplar

If <span lang="ENMathematics - Board Papers

Mark the correct RD Sharma - Volume 2

Mark the correct RD Sharma - Volume 2