Answer :

Let the points be A (k, -10, 3), B (1, -1, 3) and C (3, 5, 3).

Let us find the position vectors of these points.


Assume that O is the origin.


Position vector of A is given by,



Position vector of B is given by,



Position vector of C is given by,



Know that, two vectors are said to be collinear, if they lie on the same line or parallel lines.


Since, A (k, -10, 3), B (1, -1, 3) and C (3, 5, 3) are collinear, we can say that:


Sum of modulus of any two vectors will be equal to the modulus of third vector.


This means, we need to find .


To find :


Position vector of B-Position vector of A






Now,



…(i)


To find :


Position vector of C-Position vector of B






Now,




…(ii)


To find :


Position vector of C-Position vector of A






Now,



…(iii)


Take,



Substitute values of from (i), (ii) and (iii) respectively. We get,



Or




[ by algebraic identity, (a – b)2 = a2 + b2 – 2ab]




Squaring on both sides,




[ by algebraic identity, (a – b)2 = a2 + b2 – 2ab]









Again, squaring on both sides, we get



(48)2 + k2 – 2(48)(k) = (k2 – 6k + 234)(10) [ by algebraic identity, (a – b)2 = a2 + b2 – 2ab]


2304 + k2 – 96k = 10k2 – 60k + 2340


10k2 – k2 – 60k + 96k + 2340 – 2304 = 0


9k2 + 36k + 36 = 0


9 (k2 + 4k + 4) = 0


k2 + 4k + 4 = 0


k2 + 2k + 2k + 4 = 0


k (k + 2) + 2 (k + 2) = 0


(k + 2)(k + 2) = 0


k = -2 or k = -2


Thus, value of k is -2.


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 :

If <span lang="ENMathematics - Board Papers

A vector <span laMathematics - Exemplar

Mark (√) against RS Aggarwal - Mathematics

Define position vRD Sharma - Volume 2

Mark the correct RD Sharma - Volume 2

<span lang="EN-USRD Sharma - Volume 2

If <span lang="ENRD Sharma - Volume 2

Show that the vecRD Sharma - Volume 2

Prove that the poRD Sharma - Volume 2