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KCET2024MathematicsStraight Lines

The angle between the line x+y=3 and the line joining the points (1,1) and (-3,4) is

Options

  1. A⁻¹(7)
  2. B⁻¹ (- 1 7 )
  3. C⁻¹ ( 1 7 )
  4. D⁻¹ ( 2 7 )

Correct answer

C. ⁻¹ ( 1 7 )

Step-by-step solution

y=-x+3 ; m₁=-1= ₁ and m₂= y-1 x-1 = 4-1 -3-1 y-1 x-1 = 3 -4 ; m₂= 3 -4 = ₂ Angle between two lines are = | ₂- ₁ |= ₂- ₁ 1+ ₁ ₂ = m₂ m₁ 1+m₁ m₂ = -3 4 +1 1+ 3 4 = 1 4 4 7 Hence, | ₂- ₁ |= ⁻¹ ( 1 7 )

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