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AP EAMCET202318 May 2023Evening ShiftMathematicsVector AlgebraActual

If ( k , 1,5),(1,0,3),(7,-2, ~m ) are collinear then ( k , m )=

Options

  1. A(-2,-1)
  2. B(2,1)
  3. C(-2,1)
  4. D(2,-1)

Correct answer

A. (-2,-1)

Step-by-step solution

Points ( k , 1,5),(1,0,3) &(7,-2, ~m ) are collinear. aligned & A ( k , 1,5), B (1,0,3), C =(7,-2, ~m ) & AB =(1- k ) i +(0-1) j -2 k & AC =(7- k ) i -3 j +( m -5) k & AB = AC & (1- k ) i - j -2 k = [(7- k ) i -3 j +( m -5) k ] aligned Comparing both sides, we get aligned & 1- k = (7- k ) & -1=-3 = 1 3 & -2= ( m -5) -6= m -5 m =-1 aligned from eqn. (i) 1-k= 1 3 (7-k) aligned & 3-3 k =7- k 2 k =-4 k =-2 & ( k , m )=(-2,-1) aligned

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