AP EAMCET201920 Apr 2019Evening ShiftMathematicsThree Dimensional GeometryActual
A plane is making intercepts 2,3,4 on X, Y and Z -axes respectively. Another plane is passing through the point (-1,6,2) and is perpendicular to the line joining the points (1,2,3) and (-2,3,4) . Then angle between the two planes is
Options
- A90^
- B⁻¹ 12 61
- C⁻¹ 11 61
- D⁻¹ 5 6
Correct answer
C. ⁻¹ 11 61
Step-by-step solution
Given, X -intercept (a)=2 aligned & Y - intercept (b)=3 & Z - intercept (c)=4 aligned Equation of the plane is x 2 + y 3 + z 4 =1 aligned & B=(1,2,3) & C=(-2,3,4) aligned DR ^ S of B C =(-2,-1,3-2,4-3) =(-3,1,1) Equation of plane passing through A(-1,6,2) and having DR's (-3,1,1) is given by aligned & a (x-x₁ )+b (y-y₁ )+c (z-z₁ )=0 & -3(x+1)+1(y-6)+1(z-2)=0 & -3 x-3+y-6+z-2=0 & -3 x+y+z-11=0 aligned Angle between the planes (i) and (ii) is aligned & = |a₁ a₂+b₁ b₂+c₁ c₂ | a₁^2+b₁^2+c₁^2 a₂^2+b₂^2+c₂^2 & = |(6)(-3)