1. Sketch each of the following vectors using A and B. Label each vector. [K /4] a. -0.5A b. 2B C. 2A + 3B d. 2B - A A B 2. Consider the following vectors: a = i- 2j + 3k, b =2i - 3k, c'=-3i +2j" Compute the required vectors operations. [K /12] a. atb - c [2] b. a . b [2] c. (axb) . c [4] d. I(c x b) x al [4] 3. Consider the vector a = [A /3] a. Represent vector a graphically using a 3D box [1] b. Find the magnitude of vector a [1] c. Find the unit vector a [1] 4. If lla - bl| = lla + bl|, show that a and b are orthogonal vectors. [T /3]Indicate whether the following are vectors or scalars: [K /4] a. 40 km/h b. 120 km Northwest c. Downward force of 12 N d. Distance to the moon from Earth Considerthe parallelogram ABCD where A(0,1,2), B(1,2,3), cm, 3, 5). [A /4] a. Find the area of ABCD. [2] b. Find :13 in degrees. [2] _n Find the work done by the force F = acting at 57 to an object, when the object is moved from point A(0,1,4) to point B(3,0,5). [A [3] Suppose 17L =, 13 =, and W =. [A [4] a. Find the scalar projection of 13 on W [2] b. Find proja [2] PQRS' is a parallelogram shown below. Points T and W are the midpoints of PS and QR respectively. If PQ = LT and T5 = 13, express the following vectors as a linear combination of _- u and 13. [T /3] a. T0 P T v s