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What is the number of possible values of k for which the line joining the points (k, 1,3) and (1,-2, k+1) also passes through the point (15,2,-4) ?

Options

  1. AZero
  2. BOne
  3. CTwo
  4. DInfinite

Correct answer

C. Two

Step-by-step solution

As three points are collinear = | array ccc k & 1 & 3 1 & -2 & k+1 15 & 2 & -4 array |=0 aligned & k(8-2(k+1))+1(15(k+1)+4)+3(2+30)=0 & k(6-2 k)+(15 k+19)+96=0 & 2 k^2-21 k-105=0 aligned On solving, we will get two different values of k .

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