Dot product of two vectors `overset(rarr)A` and `overset(rarr)B` is defined as `overset(rarr)A.overset(rarr)B=aB cos phi` , where `phi` is angle between them when they are drawn with tails coinciding. For any two vectors . This means `overset(rarr)A . overset(rarr)B=overset(rarr)B. overset(rarr)A` that . The scalar product obeys the commutative law of multiplication, the order of the two vectors does not matter. The vector product of two vectors `overset(rarr)A` and `overset(rarr)B` also called the cross product, is denoted by `overset(rarr)A xx overset(rarr)B` . As the name suggests, the vector product is itself a vector. `overset(rarr)C=overset(rarr)A xx overset(rarr)B` then `C=AB sin theta` ,
A force `overset(rarr)F=3hat i +c hat j + 2 hatk` acting on a particle causes a displacement `d=4hat i+ 2 hat i + 3 hat k` . If the work done (dot product of force and displacement) is 6J then the value of c is :

Options

A. 12
B. 0
C. 6
D. 1

Answer

c

Explanation

`barw =barF.bard,6 =-12+c+6, 2c=12,c=6`