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AP EAMCET202021 Sep 2020Evening ShiftMathematicsVector AlgebraActual

If ( P =3 i +5 j - k ) and ( Q = i +2 j +3 k ) are two sides of a triangle, then its area is equal to ____ sq units.

Options

  1. A( 390 4 )
  2. B( 390 )
  3. C( 390 2 )
  4. D( 390 8 )

Correct answer

C. ( 390 2 )

Step-by-step solution

Sides of a triangle given as ( aligned & P =3 i +5 j - k and Q = i +2 j +3 k & Area of triangle = 1 2 ( P Q ) & .= 1 2 || array ccc i & j & k 3 & 5 & -1 1 & 2 & 3 array , & = 1 2 | i (15+2)- j (9+1)+ k (6-5)| & = 1 2 |17 i -10 j + k |= 1 2 289+100+1 & = 1 2 390 sq. units aligned ) Hence, option (c) is correct.

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