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Paragraph: Consider two lines whose direction ratios are (2,-1,2) and (k, 3,5) . They are inclined at an angle 4 . Question: What is the value of k ?

Options

  1. A4
  2. B2
  3. C1
  4. D-1

Correct answer

A. 4

Step-by-step solution

A(2,-1,2) B(k, 3,5) = 2 k-3+10 2^2+(-1)^2+2^2 k^2+3^2+5^2 4 = 2 k+7 3 34+k^2 = 1 2 3 34+k^2 = 2 (2 k+7) 9 (34+k^2 )=2(2 k+7)^2 306+9 k^2=8 k^2+98+56 k k^2-56 k+208=0 (k-52)(k-4)=0 k=4,52 k=4

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