MHT CET202012 Oct 2020Evening ShiftMathematicsThree Dimensional GeometryActual
The acute angle between the line r =( +2 + k )+ ( + + k ) and the plane r (2 - + k )=5 is
Options
- A⁻¹ ( 2 3 )
- B⁻¹ ( 2 3 )
- C⁻¹ ( 2 3 )
- D⁻¹ ( 2 3 )
Correct answer
A. ⁻¹ ( 2 3 )
Step-by-step solution
Given r =( i +2 j + k )+ ( i + j + k ) and the plane r (2 i - j +3 k )=5 The angle between the line r = a + b and the plane r n =p is given by = b n | b | n Here b = i + j + k | b |= 3 and n =2 i - j + k | n |= 6 Here b n =( i + j + k ) (2 i - j + k )=2-1+1=2 = 2 3 6 = 2 3 3 2 = 2 3 = ⁻¹ 2 3