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99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

If the vectors A B =p i +q j +r k , A C =s i +3 j +4 k , C B =3 i + j -2 k from A B C , then the values of p, q, r and s such that the area of that A B C is 5 6 are

Options

  1. Ap=11, q=4, r=-2, s=8
  2. Bp=8, q=4, r=2, s=5
  3. Cp=-5, q=4, r=2, s=-8
  4. Dp=14, q=4, r=2, s=11

Correct answer

B. p=8, q=4, r=2, s=5

Step-by-step solution

We have, A B =p i +q j +r k A C =s i +3 j +4 k C A =-s i -3 j -4 k and C B =3 i + j -2 k Area of A B C is 5 6 1 2 | C A C B |=5 6 ( i ) Now, C A C B = | array ccc i & j & k -s & -3 & -4 3 & 1 & -2 array |= i (6+4)- j (2 s+12)+ k (-s+9)=10 i - j (2 s+12)+ k (-s+9) 1 2 100+(2 s+12)^2+(-s+9)^2 =5 6 100+ (4 s^2+144+48 s )+ (s^2+81-18 s ) =10 6 325+5 s^2+30 s=600 5 s^2+30 s-275=0 s^2+6 s-55=0 s^2+11 s-5 s-55=0 s(s+11)-5(s+11)=0 (s+11)(s-5)=0 s-5=0 or s+11 0 s=5 Now, A B =p i +q j +r k B C =-3 i - j +2 k and C A =-s i -3

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