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BITSAT2012MathematicsThree Dimensional GeometryActual

What is the value of n so that the angle between the lines having direction ratios (1,1,1) and (1,-1, n) is 60^ ?

Options

  1. A3
  2. B6
  3. C3
  4. DNone of these

Correct answer

B. 6

Step-by-step solution

If (l₁, m₁, n₁ ) and (l₂, m₂, n₂ ) are the direction ratios then angle between the lines is = l₁ l₂+m₁ m₂+n₁ n₂ l₁²+m₁²+n₁² l₂²+m₂²+n₂² Here l₁=1, m₁=1, n₁=1 and l₂=1, m₂=-1, n₂=n and =60^ 60^ = 1 1+1 (-1)+1 n h²+1²+1² 1²+1²+y² 1 2 = 1 3 2+n² 3 (2+n² )=4 n² n²=6 n= 6

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