The edges of a parallelopiped are geven by the vectors ` (2 hat I + 3 hat j +4 hat k), 4 hat j ` and (5 hat j + mhat k). What shold be the value of m in order that the volume of the paralelopiped be 24`,

Explanation

` vec A =( 2 hat I +3 hat j + 4 hat k) , vec B =4 hat j`
and `vec C =(5 hat + m hat k)`.
Here, `vec B =0 hat I + 4 hat j + 0 hat k , vec C =0 hat I + 5 hat j + m hat k,`
Volume `V =24`.
Clearly volume of paralleleopiped id given by`
`V =|(A_(x), A_(y), A_(z)), (B_(x), B_(y), B_(z)),(C_(x), C_(y), C_(z))|= |(2, 3, 4), (0, 4, 0), (0, 5, m)|`
`=2 [4 m-0] + 3 [0 -0 ] 4 [0-0]`
`=8 m`
`:. 24 =8 m ` or `m=3`.