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AP EAMCET2015MathematicsThree Dimensional Geometry

If (2,-1,2) and (K, 3,5) are the triads of direction ratios of two lines and the angle between them is 45^ , then the value of K is

Options

  1. A2
  2. B3
  3. C4
  4. D6

Correct answer

C. 4

Step-by-step solution

Given direction ratios are (2,-1,2) and (K, 3,5) Let be the angle between two lines, then aligned & = (2,-1,2)(K, 3,5) 4+1+4 K^2+9+25 & 45^ = 2 K-3+10 9 K^2+34 & 1 2 = 2 K+7 3 K^2+9+25 & 3 K^2+34 = 2 (2 K+7) & 9 (K^2+34 )=2(2 K+7)^2 & 9 K^2+306=8 K^2+56 K+98 & K^2-56 K+208=0 K=52,4 aligned According to the given options, K=4

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