plugin-Chapter13Ex - vector ~a iare the angles α β and...

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Math 255 Additional problems from chapter 13 1. Identify the following sets. (a) r 2 - 3 z 2 = 9. (b) ρ = 4 cos φ . (c) - π 3 θ < π 2 , π 4 φ π 2 and 1 < ρ < 2. Hint: For a) and b) convert them into cartesian coordinates and use cuts to visualize the surfaces. 2. Use only the properties of the dot and cross product and ~u · ~v = 1 ~v · ~w = - 3 ~u · ~w = 0 | ~u | = 5 | ~v | = 2 | ~w | = 13 ~u × ~v = . 33 ~u + . 55 ~w ~v × ~w = - . 05 ~u + . 52 ~w ~w × ~u = . 18 ~u - . 32 ~v - . 18 ~w to compute (a) ~v · 3 ~w . (b) ~v × (2 ~w - 5 ~v ). (c) ~w · ( ~v × (2 ~u )). (d) ~v × ( ~w × ( ~v + ~u )). 3. Direction angles and direction cosines: The direction angles of a nonzero
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Unformatted text preview: vector ~a iare the angles α , β and γ (in the interval [0 ,π ] that the vector ~a makes with the positive x , y and z axis. The cosines of these angles are called the direction cosines of ~a . find a formula for the direction cosines and compute the direction angles of the vector h 4 ,-1 , 5 i . 1...
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