The following statements refer to vectors in rn (or rm/ with the standard inner product. mark each statement true or false. justify each answer. a. the length of every vector is a positive number. b. a vector v and its negative, , have equal lengths. c. the distance between u and v is ku vk. d. if r is any scalar, then krvk d rkvk. e. if two vectors are orthogonal, they are linearly independent. f. if x is orthogonal to both u and v, then x must be orthogonal to u v. g. if ku c vk2 d kuk2 c kvk2, then u and v are orthogonal. h. if ku vk2 d kuk2 c kvk2, then u and v are orthogonal. i. the orthogonal projection of y onto u is a scalar multiple of y. j. if a vector y coincides with its orthogonal projection onto a subspace w , then y is in w . k. the set of all vectors inrn orthogonal to one fixed vector is a subspace of rn. l. if w is a subspace of rn, then w