Question 10
Let i,j and k be three unit vectors along three mutually perpendicular axes, namely, the x,y and z axes respectively, and the origin O is the intersection of the three axes. At any time $t\ge 0$ after the start of an experiment, the position of a toy plane A is located along the path $\mathbf r=\mathbf i+2\mathbf j+3\mathbf k+t(3\mathbf i+5\mathbf j+2\mathbf k)$ and the position of another plane B is located along the path $\mathbf r=4\mathbf i+7\mathbf j+2\mathbf k+t(2\mathbf i+3\mathbf j+4\mathbf k)$. If d is the shortest possible distance between the two toy planes, find d².