9.) v = i +3j tk, v=-21-3j-7k- 10₁) U = -i + 3k₁ v=uj 11 U= = -1 +2j-3k, v=-i-33+k
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- Suppose that u and v are vectors in R^7 both of length 2 (squareroot of 2) and that the length of u − v is also 2 (squareroot of 2). Then ||u+v|| = ____________ and the angle between u and v is _____________.Show that there are no vectors u and v such that llull = 1, llvll = 2,and u·v= 3.Why are there no vectors u and v in R,, such that ||u.||= 2, ||v|| = 3, and uxv= -7?
- What is the value of each of the constants that are part of the linear combination between the vectors 2i+3j−k, (8, −7, 2) and (1, −1, 1) so that the vector (11 , −29, 11) is the result of that combination?Prove that llu + vll2 + llu - vll2 = 2llull2 + 2llvll2 for all vectors u and v in RnDetermine which of the vectors is parallel to z and which is orthogonal to z if z = (3, 2) Show work to verify your a) (6, -4) b) (9, 6) c) (3/2, 4) d) ( 1/3,-1/2) Parallel: Orthogonal:
- Please reply as soon as posible Consider the vectors u = (1, -8,5) and v = (- 15.0, -3)The vector w (x, 0, z) that simultaneously satisfies the following conditions:I. w * u = -3II. w = av, a ∈ RCorresponds to:a) ((-3 /2),0, (-3/10))b) ((- 5/2),0, (-1/2))c) (-15,0, -3)d) (- 3,0, (-3/5))What is the length of the vector (1, 4, 5, -3) in R^4?Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Let x3 = x1 + x2. Determine the length of x3. How does its length compare with the sum of the lengths of x1 and x2?