1. Find value(s) of m in \(\vec{v} = 4m\hat{i} + \hat{j} + 3\hat{k}\) and \(\vec{w} = 2\hat{i} + 8m\hat{j} + 6\hat{k}\) such that the vectors are
(a) parallel.
(b) orthogonal.
2. A block is placed on an inclined ramp that is parallel to \(\vec{d} = 5\hat{i} - \hat{k}\), and starts to slide down along
the ramp. The weight of the block is \(\vec{w} = -50\hat{k}\) lbs. Assume there are no other forces at play. Find
the force that is parallel to the ramp that displaces the block along the ramp.
