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 :-

Assertion (A): The torque about the point 3vec(i)-vec(j) + 3vec(k) of a force represented by 4vec(i) + 2vec(j) + vec(k) through the point 5vec(i) + 2vec(j) + 4vec(k) is vec(i) + 2vec(j)-8vec(k) Reason (R ): The torque of a force F about a point P is vec(r ) xx vec(F ) where vec(r ) is the vector from the point P to any point vec(a) on the line of action of vec(F ) Which of the following is correct ?

Find the torque of the resultant of the three forces represented by -3 vec(i) + 6 vec(j) - 3 vec(k) , 4 vec(i) - 10 vec(j) + 12 vec(k), and 4 vec(i) + 7 vec(j) acting at the point with position vector 8 vec(i) - 6 vec(j) - 4 vec(k) , about the point with position vector 18 vec(i) + 3 vec(j) - 9 vec(k) .

Find the volume of the parallelopied whose co-terminus edges are represented by the vectors vec 1= 2 hat i+ hat j- hat k, vec 2,= hat i + hat 2j+ 3hat k and vec 3 =3 hat i - hat j+2 hat k

A unit vector perpendicular to 2vec(i) + 3vec(j) + 4vec(k) and 3vec(j) + 2vec(k) is

What is the magnitude of the moment of the couple consisting of the force vec(F)=3 hat(i)+2hat(j)-hat(k) acting through the point hat(i)-hat(j)+hat(k) and -vec(F) acting through the point 2hat(i)-3hat(j)-hat(k) ?

A unit vector normal to the plane through the points vec(i), 2vec(j) and 3vec(k) is

The area of the triangle formed by thepoints whose position vectors are 3vec(i) + vec(j), 5vec(i) + 2vec(j) + vec(k) and vec(i) -2vec(j) + 3vec(k) is (in sq.u)

Find the moment of force vec(F) = 4vec(i) + 2vec(j) + vec(k) through the point 5vec(i) + 2vec(j) + 4vec(k) about the point 3vec(i) - vec(j) + 3vec(k) .

A force vec(F)= 2vec(i) + 4vec(j) + vec(k) acts on line through a point A(4, 2, -1) . Find the moment vector (torque) vec(M) " of" vec(F ) about a point P(0, 1, 2)

Find the moment of vec F about point (2,-1,3), where force vec F=3hat i+2hat j-4hat k is acting on point (1,-1,2)