Suppose that you are given nonzero vectors a, b, and c in R3. Use dot and cross products to give expressions for vectors satisfying the following geometric descriptions:
(a) A vector orthogonal to a and b
(b) A vector of length 2 orthogonal to a and b
(c) The vector projection of b onto a
(d) A vector with the length of b and the direction of a
(e) A vector orthogonal to a and b×c
(f) A vector in the plane determined by a and b and perpendicular to c.
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