Answer :

Given -





It can thus be written as:


A = (-4,2,-3)


B = (1,3,-2)


C = (-9,1,-4)


To prove – A, B and C are collinear


Formula to be used – If P = (a,b,c) and Q = (a’,b’,c’),then the direction ratios of the line PQ is given by ((a’-a),(b’-b),(c’-c))


The direction ratios of the line AB can be given by


((1+4),(3-2),(-2+3))


=(5,1,1)


Similarly, the direction ratios of the line BC can be given by


((-9-1),(1-3),(-4+2))


=(-10,-2,-2)


Tip – If it is shown that direction ratios of AB=λ times that of BC , where λ is any arbitrary constant, then the condition is sufficient to conclude that points A, B and C will be collinear.


So, d.r. of AB


=(5,1,1)


=(-1/2)Χ(-10,-2,-2)


=(-1/2)Хd.r. of BC


Hence, A, B and C are collinear


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 :

Write the directiMathematics - Board Papers

Find the angle beMathematics - Board Papers

Find the coordinaMathematics - Board Papers

Find a vector <spMathematics - Board Papers

If a line makes aMathematics - Board Papers