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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

In A B C , a point P is chosen on side A B so that A P: P B=1: 4 and a point Q is chosen on the side B C so that C Q: Q B=1: 3 . Segment C P and A Q intersect at M . If the ratio M C P C is expressed as a rational number in the lowest term as a b , then find ( a + b ) .

Correct answer

13

Step-by-step solution

Vector equation of A Q is r ₁= a + ( a - 3 c 4 ) and vector equation of C P is r ₂= c + ( c - 4 a 5 ) Hence r ₁= r ₂ gives, (1+ + 4 5 ) a = (1+ + 3 4 ) c 1+ + 4 5 =0 and 1+ + 3 4 =0 Solving, =- 1 2 and =- 5 8 aligned & p.v. of M= a - 1 2 a + 3 c 8 = 4 a +3 c 8 & M C = c - 4 a +3 c 8 = 5 c -4 a 8 aligned And PC = c - 4 a 5 = 5 c -4 a 5 aligned & M C P C = 5 8 & a=5 and b=8 ; & a+b=13 aligned

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