Q. 105.0( 1 Vote )

# Show that the fou

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 : 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 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