AP EAMCET201726 Apr 2017Morning ShiftMathematicsThree Dimensional GeometryActual
If a non-zero vector a is parallel to the line of intersection of the plane determined by the vectors j - k , 3 j -2 k and the plane determined by the vectors 2 i +3 j , i -3 j , then the angle between the vectors a and i + j + k is
Options
- A⁻¹ ( 2 3 )
- B⁻¹ ( 2 3 )
- C⁻¹ 3
- D⁻¹ ( 1 3 )
Correct answer
D. ⁻¹ ( 1 3 )
Step-by-step solution
Normal of the plane P₁ determined by the vectors j - k and 3 j -2 k , n ₁=[( j - k ) (3 j -2 k )]= | array ccc i & j & k 0 & 1 & -1 0 & 3 & -2 array |= i Normal of the plane P₂ determined by the vectors 2 i +3 j and i -3 j , aligned & n ₂=[(2 i +3 j ) ( i -3 j )] & = | array ccc i & j & k 2 & 3 & 0 1 & -3 & 0 array |= i (0)- j (0)+ k (-6-3)=-9 k aligned Since, a is parallel to the line of intersection of planes P₁ and P₂ . a= (n₁ n₂ ) = | array ccc i & j & k 1 & 0 & 0 0 & 0 & -9 array |= 9 j Now, angle between 9 j