- Math 254 Summer 2022 Take Home Exam 1 Page 3 Of 5 2 In This Question Assume That Every Vector Is 3 Dimensional The V 1 (38.44 KiB) Viewed 13 times
Math 254 Summer 2022 Take-home Exam 1 Page 3 of 5 (2) In this question, assume that every vector is 3-dimensional. The vectors 7= (1,0,0), 3= (0,1,0), and = (0,0,1) are called the standard unit vectors. (a) If = 27-3k and 5=-1+2, compute ü x 5. (b) In part (a), both vectors and 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 x . (c) Suppose & and 5 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.