Find the angle between two vectors \(A=\hat { i } +2\hat { j } -u\ and\ B=-4\hat { i } +\hat { j } -2u\)

Two bodies of mass 30 and 6g have position vectors \(2\hat { i } +\hat { j } +3u\ and\ \hat { j } +3\hat { j } +2u\)  respectively. Find the position vectors of centre of mass.

Express cross and dot product of two vectors in Cartesian coordinate.

Find the magnitude and directions of the vectors, \(\hat { i } +\hat { j } \ and\ \hat { i } -\hat { j } \)

Find the vector sum of three vectors \(\overrightarrow { A } ,\overrightarrow { B } \ and \ \overrightarrow { C } \) , using analytical method.