Q. 15.0( 2 Votes )

# In a triangle ΔOA

Answer :

Given:- , P and Q are trisection of AB

i.e. AP = PQ = QB or 1:1:1 division of line AB

To Prove:-  Proof:- Let be position vector of O, A and B respectively

Now, Find position vector of P, we use section formulae of internal division: Theorem given below

Let A and B be two points with position vectors respectively, and c be a point dividing AB internally in the ration m:n. Then the position vector of c is given by By above theorem, here P point divides AB in 1:2, so we get  Similarly, Position vector of Q is calculated

By above theorem, here Q point divides AB in 2:1, so we get  Length OA and OB in vector form    Now length/distance OP in vector form       length/distance OQ in vector form       Taking LHS

OP2 + OQ2

= = as we know in case of dot product  Angle between OA and OB is 90°,  Therefore, OP2 + OQ2

= = = = As from figure OA2 + OB2 = AB2

= = RHS

Hence, Proved.

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 :

Write a unit vectMathematics - Board Papers

Fill in the blankMathematics - Exemplar

A and B areMathematics - Board Papers

L and M are two pMathematics - Board Papers

The scalar producMathematics - Board Papers

A vector <span laMathematics - Exemplar