Direction: Solve the following completely. Include your graph. Write your Solutions
in short bond paper with margin 1 inch in all sides.

1. Given: A = Axax + 3ay - 2az
B = 4ax + Byay + 8az
a. Find Ax and By if A and B are parallel.
b. What is the relation between Ax + By if A is normal to B.

2. Given two points A(5,4,3) and B(2,3,4). Find:
a. A+B
b. A●B
c. θAB
d. AxB
e. Unit vector parallel to the plane containing A nad B
f. Area of the parallelogram of which A and B are adjacent sides.

3. E and F are vector fields given by E = 2xax + ay + yzaz and F = xyax — y2ay+
xyzaz. Determine:
a. |E|at(l,2, 3)
b. The component of E along F at (1, 2, 3)
c. A vector perpendicular to both E and F at (0, 1,-3) whose magnitude is
unity

4. Given A = x2yax — yzay + yz2az, determine:
a. The magnitude of A at point T(2, -1,3)
b. The distance vector from T to S if S is 5.6 units away from T and in the same
direction as A at T
c. The position vector of S

5. During a ground test, a 400 N aerodynamic force is applied to the tail rotor of the
helicopter at P as shown. Determine the moment of the forve about point O of the
airframe.