4. (a) Prove, without recourse to geometry, that u • (v × w) = v • (w × u) = w • (u × v) = −u • (w × v) = −w. (v xu) = -v (u x w).

Find the distance from the point (8,-2,-4) to the line ä(t) = (-1,-4, 1)t + (-5,5,8).

Two archers will simultaneously shoot once at a target. Let Xi , i = 1, 2, be marksman i's horizontal error, measured in meters. If the target's position is (a, b), and marksman i's shot ends up at (x, y), then Xi = (x - a). These errors are modeled by X1 ~ N(0, 0.5) and X2 ~ N(0, 1). What is the probability that both shots will be within 1 meter of the target, in the horizontal direction?