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JEE Main20249 Apr 2024Evening ShiftMathematicsVector AlgebraActual

Between the following two statements: Statement I : Let a = i +2 j -3 k and b =2 i + j - k . Then the vector r satisfying a r = a b and a r =0 is of magnitude 10 . Statement II : In a triangle A B C, 2 A+ 2 B+ 2 C - 3 2 .

Options

  1. AStatement I is incorrect but Statement II is correct.
  2. BBoth Statement I and Statement II are correct.
  3. CStatement I is correct but Statement II is incorrect.
  4. DBoth Statement I and Statement II are incorrect.

Correct answer

A. Statement I is incorrect but Statement II is correct.

Step-by-step solution

aligned & a = i +2 j -3 k & a =2 i + j - k & a r = a b ; a r =0 & a ( r - b )= 0 & a = ( r - b ) & a a = ( a r - a b ) & 14=-7 =-2 & - a 2 = r - b r = b - a 2 & = 2 b - a 2 = 3 i + k 2 aligned Statement (I) is incorrect aligned & 2 ~A + 2 ~B + 2 c - 3 2 & 2 ~A +2 ~B +2 C =2 & 2 ~A + 2 ~B + 2 C & =-1-4 A B C & -1-4 1 2 1 2 1 2 & =- 3 2 aligned Statement (II) is correct.

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