8. a. Using the vectors = (3, 3, 1) and ỷ = (-1, 2, –3), verify that the following formula is true: ỷ = + ỷ|² – – 3/² 4 b. Prove that this formula is true for any two vectors.

Q: 81. Given r = (-3, 4) and s = a. Find the product ||r|||s||. (9. – 12). b. Find r· s. c. Based on…

A: Given:r=-3,4 and s=9,-12Formula:u=u.u

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

Q: would the two vectors be (1 1 1 0) and then (0 0 0 1)?

A:

Q: 2. For the vectors u = -5i + k and v = 3j - 4k, find a. (u · v)u b. u - 3v

A:

Q: Find all vectors u that satisfy the equation (1,1,1) xu = (6,- 5,- 1). Select the correct choice…

A: To find all vectors u that satisfy the given equation

Q: For the vectors A = Ux + 3uy + 5uz , B = 2ux, 4uy + 6uz, and C = 3ux + 4uy + 5uz. Show that A x (B x…

A: For the vectors A = Ux + 3uy + 5uz , B = 2ux, 4uy + 6uz, and C = 3ux + 4uy + 5uz. To show :-A x (B x…

Q: The vector result of (ì − 2j +3k) · (−2ī + 2j − 2k) is a. -i + 7j b. -i+j-k d. j+7k e. -i+7k c.…

A:

Q: Graph the two vectors x= (5, 1,3) and y=(-1,3,1

A: Topic:- 3D

Q: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

Q: {0·0·0} - {0·8·0} - {0···0} II. I only B II only CI and II only DI and III only

A:

Q: Consider the following points. A(3, 1, 1), B(4, -4, 6), C(7, -2, 0), D(6, 3, −5) Let u = AB, VAC,…

A: Consider the following points.Let , , and . Find each of these vectors.Find the scalar triple…

Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

A:

Q: 3.2.1 Vector Cross Product Let vectors: A = (1, 0, −3), B = (–2, 5, 1), and C = (3, 1, 1). Part…

A: Since, you have posted a question with sub-parts greater than three. We will provide the solution…

Q: Let i = [1 -4] and y = [4 -6]. Find the following vectors. i = 57 ü = 2g =| w = 5i + 2j =||

A: The solution is given below:-

Q: Place the vectors a, b, c, and d in order of length, from smallest to largest. Show your…

A: We have to find length of each vectors first.

Q: 2. Consider the vectors =(1,2,3,0),= (0,1,2,3) and = (2,3,4,-3) Let = (1,1,1,1) (a) Is a linear…

A:

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

A:

Q: Let = (1,2) and 7=(3, a) be two vectors in R². (a) For which value of a the two vectors an are…

A: Vector is parallel to another iff one is constant multiple of other .example: u=kv Orthogonal when…

Q: Let the vectors x = (-0.3, –4.6, –3) and y = (4.1, –-2.2, r) Determine the value of r such that the…

A:

Q: are parallel, orthogonal, or Determine whether vectors V and W neither. If parallel, determine…

A:

Q: For the vectors u = (1, 2, 0) and v = (2, 1, 3) , evaluate the following expressions. a. 2u + 4v c.…

A:

Q: 1. Given the vectors à = (-1, 1, 1), b = (2, 1, –3), and ở = (5, 1, –-7), calculate the value of…

A: Note:- according to the company policy we can attempt only three subparts of a question so please…

Q: If c = 14, is the vector 2i + 5j in the span of ci – 12j and 7i - 6j? If c # 14, is the vector 2i +…

A: Answer

Q: 1. a. If 37-2ỷ = ở and 5x - 33 = b, express the vectors and y in terms of a and b. %3D %3D

A: