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 bodies of masses 2 kg and 3 kg have position vectors hat(i) + 2 hat (j) + hat(k) and -4hat(i)-3 hat(j) + 6 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.

Find the angle between the vectors hat i - 2 hat j + 3 hat k and 3 hat i - 2 hat j + hat k .

Find λ if the vectors hat i-hat j+ hat k, 3 hat i+ hat j+ 2 hat k and hat i+ λ hat j- 3 hat k are coplanar.

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.

The unit vector in the direction of the sum of vectors hat i + hat j + hat k and 2 hat i + 3 hat j + 4 hat k is

Find the image of the point having position vector hat i+2 hat j+4 hat k in the plane vec r.(2 hat i- hat j+ hat k)+3=0.

Prove that the vectors 2 hat i- hat j+ hat k , hat i- 3 hat j- 5 hat k and 3 hat i- 4 hat j- 4 hat k are coplanar.

Show that the points whose position vectors are 5hat i+5hat k,2hat i+hat j+3hat k and -4hat i+3hat j-hat k are collinear