MHT CET202124 Sep 2021Evening ShiftMathematicsVector AlgebraActual
If a + b , b + c , c + a are coterminous edges of a parallelepiped, then its volume is
Options
- A0
- B4[ b a c ]
- C3[ a c b ]
- D2[ a b c ]
Correct answer
D. 2[ a b c ]
Step-by-step solution
The volume of required parallelepiped aligned & =( a + b ) [( b + c ) ( c + a )] & =( a + b ) [( b c )+( b a )+( c c )+( c a )] & =[ a ( b c )]+[ a ( b a )]+0+[ a ( c a )] & +[ b ( b a )]+0+[ b ( c a )] & =[ a ( b c )]+0+0+0+0+0+0+[ b ( c a )] & =2 a ( b c ) aligned