ECE 280 Homework 1 Due:January 19, 2009 1.Given vectorsand , determine: ˆ3A=+xrˆzˆzˆˆ526B=+−xyra)AB+rrb)5AB−rrc)The component of Aalong ˆyd)A unit vector parallel to3AB+rr. 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 ˆ3AxzrˆˆzBrABθ. b) Decompose Arinto components parallel and perpendicular to Br. 4.If ˆ234Arzand ˆ64B=−−+rz, find the scalar and vector componentsof along the direction of CAB=×rrrˆDxyz=−+r. 5. Given the vectors 222A=−+xˆyzvand 123Bˆ=xyzv, find a unit vector perpendicular to both and AvBv. (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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