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KCET2024MathematicsThree Dimensional Geometry

The sine of the angle between the straight line x-2 2 = y-3 4 = 4-z 2 are the plane 2 x-2 y+z=5 is

Options

  1. A1 5 2
  2. B2 5 2
  3. C3 50
  4. D3 50

Correct answer

A. 1 5 2

Step-by-step solution

We have, the equation of line as x-2 3 = y-3 4 = 4-z -5 x-2 3 = y-3 4 = z-4 5 This line is parallel to the vector b =3 i +4 j +5 k Equation of plane is 2 x-2 y+z=5 Normal to the plane is n =2 i -2 j + k Then, = b n | b || n | = |(3 i +4 j +5 k ) (2 i -2 j + k )| 3^2+4^2+5^2 4+4+1 = |6-8+5| 50 9 = 3 15 2 = 1 5 2

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