Moment about point whose coordinate is (1,2,3) of a force represented by `vec(i)+vec(j)+vec(k)` acting at the point (-2,3,1) is :-

Options

A. `6vec(i)+2vec(j)-8vec(k)`
B. `vec(i)`
C. `-3vec(i)-2vec(j)+4vec(k)`
D. `3vec(i)+vec(j)-4vec(k)`

Answer

D

Explanation

`vec(tau)=vec(r)xxvec(F)=( vec(r)_(1)-vec(r)_(0))xxvec(F)`
`=(-3hat(i)+hat(j)-2hat(k))xx(hat(i)+hat(j)+hat(k))`
`={:|(hat(i),hat(j),hat(k),),(-3,1,-2,),(1,1,1,)|=3hat(i)+hat(j)-4hat(k)`