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CBSE Class 11-science Answered

OA, OB and OC represent in magnitude and direction three vectors P, Q and R. If P + Q = 2R, prove that C is the midpoint of AB.

Asked by shamparana.rana1 | 09 Sep, 2019, 07:16: PM
Expert Answer
Let position vectors of  A, B, C  are P, Q, R as shown in figure .
 
vector AC = R - P  .....................(1)
 
vector CB = Q - R  ......................(2)
 
It is given that ,  P + Q = 2R  ..........(3)
 
Eqn. (3) can be written as, Q - R = R - P  ......................(4)
 
Hence   from eqn.(4), eqn.(1) and eqn.(2), we get  vector AC = vector CB 
 
Since A, B and C are colinear points, then we get C is mid point of AB
Answered by Thiyagarajan K | 09 Sep, 2019, 09:48: PM
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