(Solved): 1. Consider the points in the plane shown here: (a) Which vector, with initial point M, is equal t ...

1. Consider the points in the plane shown here: (a) Which vector, with initial point $M$, is equal to ${\mathrm{proj}}_{\overrightarrow{LB}}(\overrightarrow{PT})$, the projection of $\overrightarrow{PT}$ onto $\overrightarrow{LB}$ ? (b) What is ${\mathrm{proj}}_{\overrightarrow{EM}}(\overrightarrow{GM})$, the projection of $\overrightarrow{GM}$ onto $\overrightarrow{EM}$ ? (c) Which direction does the cross product $\overrightarrow{MI}\times \overrightarrow{MS}$ point in? (d) What is the magnitude of the cross product $\overrightarrow{LW}\times \overrightarrow{LS}$ ? (The points are all equally spaced apart at intervals of one unit between horizontally and vertically adjacent points.)