What is the torque of the force `vecF=3hati-2hatj+4hatk` acting at a point `vecr=2hati+3hatj+5hatk` about the origin?

A force vecF= alpha hat i +3 hatj+6hatk is acting at a point vec r =2hati-6hatj-12 hatk .The value of alpha for which angular momentum about origin is conserved is:

If the resultant of three forces vecF_1 = p hati + 3hatj -hatk, vecF_2 = 6hati-hatk and vecF_3 =-5hati +hatj +2hatk acting on a particle has a magnitude equal to 5 units, then the value of p is

Find the vector equation of the plane passing through the intersection of the two planes vecr(hati+hatj+hatk)=6 and vecr(2hati+3hatj+4hatk)=-5 and through the point (1,1,1)

Find the vector equation of the plane pass ing through the intersection of the planes vecr.(hati+hatj+hatk)=6 and vecr.(2hati+3hatj+4hatk)=-5 , and the point (1,1,1).

Show that the lines vec r = hati + hatj + t(hati - hatj +3hatk) and vecr = 2hati + hatj -hatk + s(hati + 2hatj -hatk) intersect . Find the point of intersection.

If the resultant of three forces vecF_1= phati +3hatj-hatk , vecF_2 =-5hati+hatj+2hatk and vecF_3= 6hati -hatk acting on a particle has a magnitude equal to 5 units, then what is difference in the values of p ?

The co-ordinates of the point P on the line vecr =(hati +hatj + hatk)+lambda (-hati +hatj -hatk) which is nearest to the origin is