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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

Let A =2 i + j +5 k and B =x i +y j +z k If A B =11 ; A B =-13 i -9 j +7 k , then: [Note: [k] denotes greatest integer function less than or equal to k .]

Options

  1. Ax^2+y^2=10
  2. By^2+z^2=13
  3. C[x+y+z]=5
  4. Dx+y z =2

Correct answer

B. y^2+z^2=13

Step-by-step solution

A B =-13 i -9 j +7 k Take cross with A A ( A B )= A (-13 i -9 j +7 k )( A B ) A -| A |^2 B = | array ccc i & j & k 2 & 1 & 5 -13 & -9 & 7 array |=52 i -79 j -5 k aligned & 11 A -30 B =52 i -79 j -5 k & (22-30 x) i +(11-30 y) j +(55-30 z) k =52 i -79 j -5 k aligned Now, comparing coefficients of i , j and k , we get array lll 22-30 x=52 & & x=-1 11-30 y=-79 & & y=3 55-30 z=-5 & & z=2 array Now, verify.

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