Q. 13

# Find the value of λ for which the four points with position vectors and are coplanar.

Given :

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

To Find : value of λ

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(2 + 2λ) – 0 + 2(4)

= - 4 - 4λ + 8

= 4 – 4λ

………eq(4)

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

………eq(5)

From eq(4) and eq(5)

4 – 4λ = 0

4λ = 4

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Questions Based on 3D Geometry26 mins
Questions Based on 3D Geometry | Check Yourself40 mins
Lecture on Product of Determinants58 mins
Meselson and Stahl experiment49 mins
DNA Fingerprinting42 mins
NEET 2021 | Transcription - An important Topic62 mins
Microsporogenesis & Megasporogenesis49 mins
Interactive Quiz on Microbes in Human Welfare29 mins
Interactive Quiz on Molecular basis of Inheritance-0234 mins
Medelian disorder series: Thalassemia, Sickle cell anaemia & Phenylketonuria60 mins
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