MHT CET202121 Sep 2021Morning ShiftMathematicsVector AlgebraActual

The vertices of triangle ABC are A (3,0,0) ; B (0,0,4) ; C (0,5,4) . Find the position vector of the point in which the bisector of angle A meets BC is

Options

A5 i +12 j
B5 i +12 k 3
C5 i +12 j 13
D5 i -12 j 3

Correct answer

B. 5 i +12 k 3

Step-by-step solution

Let AD be the angle bisector of angle A which divides BC in the ratio AB : AC Here AB = 9+16 = 25 and aligned & AC = 9+25+16 & = 50 aligned D divides BC in the ratio 25 : 50 i.e., 1: 2 Position vector of D = (4)(2) k +5 j +4 k 1+2 = 5 j +12 k 3

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