Q. 35.0( 5 Votes )

If <span lang="EN

Answer :

Given the position vectors of points A and B are and.

Let the position vectors of points C and D be and.

We have AC = 3AB.

From the above figure, observe AB = AC – BC

AC = 3 (AC – BC)

AC = 3AC – 3BC

2AC = 3BC

AC : BC = 3 : 2

So, C divides AB externally in the ratio 3:2.

Recall the position vector of point P which divides AB, the line joining points A and B with position vectors and respectively, externally in the ratio m : n is

Here, m = 3 and n = 2

So, the position vector of C is

We also have BD = 2BA.

From the figure, observe BA = BD – AD

BD = 2 (BD – AD)

BD = 2BD – 2AD

BD = 2AD

BD : AD = 2 : 1

So, D divides BA externally in the ratio 2:1.

We now use the same formula as earlier to find the position vector of D.

Here, m = 2 and n = 1

Thus, the position vector of point C is and the position vector of point D is .

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

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