If `veca=a_(1)hati+a_(2)hatj+a_(3)hatk, vecb= b_(1)hati+b_(2)hatj + b_(3)hatk, vecc=c_(1)hati+c_(2)hatj+c_(3)hatk` and `[3veca+vecb \ \ 3vecb+vecc \ \ 3vecc + veca] =lambda|{:(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3):}| " then find the value of " lambda/4`

Answer

7

Explanation

`veca=a_(1)hati=a_(2)hatj +a_(3)hatk`
`vecb=b_(1)hati+b_(2)hatj+b_(3)hatk`
`vecc = c_(1)hati +c_(2)hatj +c_(3)hatk`
L.H.S = ` [3veca +vecb 3vecb+vecc 3vecc +veca]`
`[3veca 3vecb 3vecc] + [vecb vecc veca]`
`3^(3)[veca vecb vecc] + [veca vecb vecc]`
`28 [veca vecb vecc]`