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Vector Quiz #1 Name:_________________________ Calculator Allowed. You must show enough work to enable me to recreate your results. 1. Find all value(s) of a such that a, 2a is a unit vector. We want 2. a 2 2a 1 5a 2 1 a 2 1 5 5 5 A pilot sets her plane to fly on “autopilot” in the direction N30W at a speed of 400 mph. A few minutes later, she checks the instruments and discovers that, due to the wind, the plane has actually been flying in the direction N10W at 430 mph. What is the speed and direction of the wind? Support your results with a picture. IMSA Vectors - 1 F12 3. In triangle ABC, Y is the midpoint of AB , 1 AX AC , and Z is the midpoint of BX . 3 Find the following vectors in terms of v AX and w AY . B Y Z w A a. AC 3v c. CX 2v C X v b. BC BA AC 2w 3v d. XZ : 1 AX 2 XZ AB XZ AB AX 2 1 2w v 2 1 w v 2 4. Given the vectors v 4, 4 and w 1,2 , find the following: a. v 16 16 4 2 b. v 2w 2,0 2 c. vˆ 1 1 v 4, 4 v 4 2 1 1 , 2 2 d. Sketch w and find the angle between w and the positive x-axis. d. Find the vector of length 3 units in the direction of v . 3 3 , This would be 3vˆ 2 2 IMSA Vectors - 2 F12