(2) In this question, assume that every vector is 3-dimensional. The vectors i = (1,0,0), 3= (0,1,0), and k (0,0,1) are

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2 In This Question Assume That Every Vector Is 3 Dimensional The Vectors I 1 0 0 3 0 1 0 And K 0 0 1 Are 1 (57.45 KiB) Viewed 8 times

(2) In this question, assume that every vector is 3-dimensional. The vectors i = (1,0,0), 3= (0,1,0), and k (0,0,1) are called the standard unit vectors. (a) If u = 27-3k and =-+2k, compute u x . (b) In part (a), both vectors u and 7 can be written using the same two standard unit vectors, even though they are 3-dimensional. Describe the plane that both of these vectors are in, and relate that plane to the direction of ü x v. (c) Suppose a and 6 are any two non-parallel vectors that are defined in terms of two standard unit vectors. How many standard unit vectors are needed to write axb? Justify your answer geometrically or by using the equation of the cross product.