The position vectors of two balls are given by
`vec(r )_(1)=2 (m)i+7(m)j`
`vec(r )_(2)= -2(m)i+4(m)j`
What will be the distance between the two balls?

The position vectors of two balls are given by vec(r)_(1)=2hat(i)+7hat(j) , vec(r)_(2)=-2hat(i)+4hat(j) What will be the distance between the two balls?

The position of the particle is given by vec(r )=(vec(i)+2vec(j)-vec(k)) momentum vec(P)= (3vec(i)+4vec(j)-2vec(k)) . The angular momentum is perpendicular to

Two particles having position vectors vec(r )_(1) = ( 3 hat(i) + 5 hat(j)) meters and vec( r)_(2) = (- 5 hat(i) - 3 hat(j)) metres are moving with velocities vec(v)_(1) = ( 4 hat(i) + 3 hat(j)) m//s and vec(v)_(2) = (alpha hat(i) + 7 hat(j)) m//s . If they collide after 2 s , the value of alpha is

The position vectors of the vertices of a triangle are vec(i) +2 vec(j) +3 vec(k) , 3 vec(i) -4 vec(j) +5 vec (k) and -2vec (i) +3 vec (j) - 7 vec (k) Find the perimeter of a triangle .

The position vectors of three particles of mass m_(1)= 1kg, m_(2)=2 kg and m_(3)=4 kg are vec(r )_(1)=(hat(i)+4hat(j)+hat(k))m, " " vec(r )_(2)=(hat(i)+hat(j)+hat(k))m , and vec(r )_(3)=(2hat(i)-hat(j)-2hat(k))m respectively. Find the position vector of their centre of mass.

The position vectors of two point masses 10 kg and 5 kg are (-3vec(i)+2vec(j)+4vec(k))m " and " (3vec(i)+6vec(j)+5vec(k))m respectively. Locate the position of centre of mass.

An object has a displacement from position vector vec(r )_(1)=(2hat(i)+3hat(j))m to vec(r )_(2)=(4hat(i)+6hat(j))m under a force vec(F)=(3x^(2)hat(i)+2y hat(j))N . Find the work done by this force.

Two balls of mass m each are hung side by side by side by two long threads of equal length l. If the distance between upper ends is r, show that the distance r' between the centres of the ball is given by g r'^(2)(r-r')=2l G m