Write two different vectors having same magnitude.

Find the unit vector in the direction of vector , where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively

Find the unit vector in the direction of the vector \( \vec{a}=\hat{i}+\hat{j}+2\hat{k}\)

Find the sum of the vectors 

Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).

Find the values of x and y so that the vectors \( 2\hat{i}+3\hat{j}\) and \( x\hat{i}+y\hat{j}\) are equal