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Question
The points with position vectors 60^i+3^j, 40^i−8^j, a^i−52^j are collinear if
The points with position vectors 60^i+3^j, 40^i−8^j, a^i−52^j are collinear if
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Solution
The correct option is A a=−40
suppose 60i+3j , 40i−8j and ai−52j is the three position of vector A,B,C
−−→AB=(40i−8j)−(60i+3j)−−→AB=−20i−11j−−→BC=(ai−52j)−(40i−8j)−−→BC=(a−40)i−44j(a−40)i−44j=m(−20i−11j)(a−40)i−44j=−20im−11jm−44=−11mm=−44−11m=4a−40=−20ma−40=−20(4)a=−80+40a=−40
suppose 60i+3j , 40i−8j and ai−52j is the three position of vector A,B,C
−−→AB=(40i−8j)−(60i+3j)−−→AB=−20i−11j−−→BC=(ai−52j)−(40i−8j)−−→BC=(a−40)i−44j(a−40)i−44j=m(−20i−11j)(a−40)i−44j=−20im−11jm−44=−11mm=−44−11m=4a−40=−20ma−40=−20(4)a=−80+40a=−40
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