Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Which of the followings is/are correct :

Options

AThe angle between the two straight lines r =3 i -2 j +4 k + (-2 i + j +2 k ) and r = i +3 j -2 k + (3 i -2 j +
B( r . i )( i r )+( r . j )( j r )+( r . k )( k r )= 0 .
CThe force determined by the vector r =(1,-8,-7) is resolved along three mutually perpendicular directions, one
DThe cosine of the angle between any two diagonals of a cube is 1 3 .

Correct answer

D. The cosine of the angle between any two diagonals of a cube is 1 3 .

Step-by-step solution

A : Angle between the given lines is = angle between the vectors (-2 i + j +2 k ) and (3 i -2 j +6 k ) = (-2 i + j +2 k ) (3 i -2 j +6 k ) |-2 i + j +2 k ||3 i -2 j +6 k | = ⁻¹ ( 4 21 )B: Let ( r =x i +y j +2 k ) r =x i +y j +2 k given expression is x[y k -z j ]+y[z i -x k ]+z[x j -y i ]= 0 C: Component of r in direction of a = r a | a | a = ( i -8 j -7 k ) (2 i +2 j + k ) 3 (2 i +2 j + k ) 3 =- 21 9 (2 i +2 j + k )=- 7 3 (2 i +2 j + k ) D : Dr's of diagonal BD = a ,- a , a or 1,-1,1 Dr's of diagonal AF =- a , a ,

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