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Question 1. (a) Find the magnitude of the vector w~ =~ i + 3~ j −~ k. (b) Find the direction cosines of the vector w~ =~ i−2~ j −~ k. (c) Calculate 2~u+~v−w~, if ~u =~ i+2~ j−2~ k, ~v =~ i+4~ j−~ k and w~ =~ i−~ j+3~ k.
Question 2. Let ~u =~ i−~ j + 2~ k, ~v = 2~ i−3~ j +~ k. (a) Calculate the dot product of ~u and ~v.
(b) Find the cross product of ~u and ~v.