Q. 35.0( 5 Votes )

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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 .


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