Two bodies of `6kg` and `4kg` masses have their velocity `5hati - 2 hat j + 10 hat k` and `10hat i - 2 hat j + 5 hat k` respectively. Then, the velocity of their centre of mass is

Two bodies of masses 10 kg and 2 kg are moving with velocities 2 hat(i)-7 hat(j)+3 hat(k) and -10 hat(i)+35 hat(j)-3hat(j) ms^(-1) respectively. Find the velocity of the centre of mass of the system.

Two bodies of mass 1 kg and 3 kg have position vectors hat i+ 2 hat j + hat k and - 3 hat i- 2 hat j+ hat k , respectively. The centre of mass of this system has a position vector.

Two blocks of mass 1kg and 3 kg have position v ectors hat(i) + 2 hat(j) + hat(k) and 3 hat(i) - 2 hat(j) + hat(k) , respectively . The center of mass of this system has a position vector.

Two particles of mass 1 kg and 3 kg have position vectors 2 hat i+ 3 hat j + 4 hat k and -2 hat i+ 3 hat j - 4 hat k respectively. The centre of mass has a position vector.

the angle between the vectors 2hat i-3hat j+2hat k and hat i+5hat j+5hat k is

The position vectors of the vectices A, B, C of a triangle ABC " are " hati - hat j - 3 hat k , 2 hati + hat j - 2 hat k and - 5 hati + 2 hat j - 6 hat k respectively. The length of the bisector AD of the angle angle BAC where D is on the line segment BC, is

The angle between the two vectors vec A= 3 hat i + 4 hat j + 5 hat k and vec B = 3 hat i + 4 hat j + 5 hat k will be

Find the angul between two vectors A= 2 hat j + hat j - hat k and B=hat j - hat k and B = hati - hatk .

Prove that point hat i+2hat j-3hat k,2hat i-hat j+hat k and 2hat i+5hat j-hat k from a triangle in space.

Prove that the points hat i-hat j,4hat i-3hat j+hat k and 2hat i-4hat j+5hat k are the vertices of a right angled triangle.