Question

Recall from linear algebra the definition of the projection of one vector onto another. As before, we have 3-dimensional vectors = a2 a3 and (2) -a2 - a3 What is the signed magnitude c of the projection pf)-r2) of x1) onto a(2)? More precisely, let u be the unit vector in the direction of the correct choice above, find a number c such that pri)-g(2) == CU. Express your answer in terms of a 1 for a1, a_2 for a2, and a_3 for a3. C= What is the (vector) projection p, 0)p(?) of x(1) onto a(2)? Express your answer in terms of the signed magnitude c, (1), ||x(1)||, x2), ||x2)||. (Enter x1 for ), norm(x1) for ||21)||. will work independently. For proper display, enclose x1 and x2 by brackets, e.g. (x1). x2 for 2) and norm(x2) for ||(2 |. Do not worry if the parser does not display properly, the grader (Input update:In the last question, the grader has been updated to accept answers in terms of c instead of norm(p). Earlier correct answers will remain correct.) Pr)(2)=

Answer 1

onto 2) bvofection vector The where u the unit x vector the directiDn ataas igned magnitude Hence the 2 ai- aas 2

of nto x D The projection veetor 2) he e fhe operator dot denotes product a