Homework_1 - ECE 280 Homework 1 Due: January 19, 2009 r r...

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ECE 280 Homework 1 Due: January 19, 2009 1. Given vectors and , determine: ˆ 3 A =+ x r ˆ z ˆ z ˆˆ 526 B =+− xy r a) AB + r r b) 5 A B r r c) The component of A along ˆ y d) A unit vector parallel to 3 A B + r r . 2. An airplane has a ground speed of 350 km/hr in the direction due west. If there is a wind blowing northwest at 40 km/hr, calculate the true air speed and direction of the airplane. 3. a) If and , find ˆ 3 A xz r ˆ ˆ z B r AB θ . b) Decompose A r into components parallel and perpendicular to B r . 4. If ˆ 234 A r z and ˆ 64 B =− + r z , find the scalar and vector components of along the direction of CAB rr r ˆ Dxyz = −+ r . 5. Given the vectors 222 A =−+ x ˆ y z v and 123 B ˆ = x y z v , find a unit vector perpendicular to both and A v B v . (Hint: Use the cross product .) 6. The vertices of a triangle are given by the points P(1,1,0), Q(4,2,0), and R(2,5,0). Find the three interior angles of the triangle. (Hint: assign vectors to each side of
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