Find the magnidude and direction cosines of the torque of a force represented by `3hat(i)+4hat(j)-5hat(k)` about the point with position vector `2hat(i)-3hat(j)+4hat(k)` acting through a point whose position vector is `4hat(i)+2hat(j)-3hat(k).`

Find the torque of the resultant of the three forces represented by -3hat(i)+6hat(j)-3hat(k),4hat(i)-10hat(j)+12hat(k)and4hat(i)+7hat(j) acting at the point with position vector 8hat(i)-6hat(j)-4hat(k), about the point with position vector 18hat(i)-3hat(j)-9hat(k).

Find the torque of a force 7 hat(i) + 3 hat(j) - 5 hat(k) about the origin. The force acts on a particle whose position vector is hat(i) - hat(j) + hat(k)

Find the vector and Cartesian equations of the plane passing through the point with position vector 2hat(i)+6hat(j)+3hat(k)" and normal to the vector "hat(i)+3hat(j)+5hat(k).

The angle between the vector 3hat(i)+4hat(j)+5hat(k) and the z-axis is

Forces of magnitude 5sqrt(2)and10sqrt(2) units acting in the directions 3hat(i)+4hat(j)+5kand10hat(j)+6hat(j)-8hat(k), respectively, act on a particle which is displaced from the point with position vector 4hat(i)-3hat(j)-2hat(k) to the with position vector 6hat(i)+hat(j)-3hat(k). Find the work done by the forces.

Show that the points whose position vectors are 2hat(i) + 3hat(j) - 5hat(k), 3hat(i) + hat(j) - 2hat(k) and 6hat(i) - 5hat(j) + 7hat(k) are collinear.

Find the direction cosines and direction ratios for the following vectors. 3hat(i)-3hat(k)+4hat(j)