Vectors Questions and Answers

12 Vector u has components 3 2 2 and vector v has components 1 2 3 find the angle 8 between u and v and then find the component vector of u that is perpendicular to vector v

Let f be the function shown below The function f has a domain of 8 1 and a range of 1 2 10 8 i Domain ii Range c Suppose the function j is given as j x Preview Preview 15 8 6 4 Beauian 24 a Suppose the function g is given as g x f x 5 Determine the domain and range of g i Domain Preview Preview ii Range b Suppose the function h is given as h z 2f z Determine the domain and range of h 2 4 6 f x Determine the domain and range of j

6 Graphing a cosecant function using transformations 21 points csc 3x y 1 State the parent function y csc x 1 point 2 Give the full description of the transformations that were applied to its graph 4 points 3 State the period 4 State the domain 5 State the range WE 1 point In x 3 any integer n 00 U Z100 2 point For 2 points 6 List the coordinates of the two key points and their images after each transformation setup a table with transformations and images 3 points Functions MATH BB 7 Graph the function Show at least two periods 6 points 8 Show asymptotes as dashed lines and label them 1 point 9 Label the key points 1 point H 10 Trigonometr

(i) Calculate g(K7) and g(K11). (ii) Give an example of a complete graph of genus 2.

A pilot is flying at 10,000 feet and wants to take the plane up to 20,000 feet over the next 50 miles. What should be his angle of elevation to the nearest tenth?

Given is the fact that the set of vectors a, b, c of a vector space is independent. Which of the following sets of vectors is/are dependent? 5a+5b+4c, 5b+5c, -5a-10b-9c a, b, -4a-4b+5c 5a+5b+4c, 5b+5c,3b b, b+c, 5b+5c

Let T: R³ → R³ be a linear transformation such that: T(1,0,0)=(4, -2, 1) T(0,1,0)=(5,-3,0) T(0,0,1)=(3,-2,0) Find T(3, -5,2).

Give the vector equation of a line perpendicular to the line 1: x=2t-1, y=-3t, t€ R. Are there other answers?

Assume that T is a linear transformation. Find the standard matrix of T. T:R² - R² first rotates points through -5π/6 radians and then reflects points through the horizontal x₁-axis A= (Type an integer or simplified fraction for each matrix element. Type exact answers, using radicals as needed)

A vector has a magnitude of 20 in the 30° direction. What are the horizontal and vertical components of this vector?

The lines r= (-3, 8, 1) + s(1, -1, 1), S∈R, and r = (1, 4, 2) + t(-3, k, 8), t∈R, intersect at a point. a. Determine the value of k. b. What are the coordinates of the point of intersection?

Consider the following vectors: u= 0 v= 1 w= 1 x= 3 1 -2 0 -6 2 0 4 0 Which of the following statements are true? (select all correct answers) A) Vector x lies in the plane spanned by v and w. B) Vector w lies in the plane spanned by u and v. C) Vector x lies in the plane spanned by u and v. D) Vectors u, v and w span a plane. E) Vector w is not a linear combination of u and v.

Determine the parametric equations of a line passing through the point P(3,2,-1) and with a direction vector perpendicular to the liner r=(2,-3,4) + s(1, 1,-2), s ∈ R.

Given: ΔABC, AB= 2,AC = 6, M and P are midpoints of AB and AC. m∠BAC = 60° BP and CM intersect at O Using vectors without going to coordinates find cos ∠COP. Must provide a sketch.

Darla purchased a new car during a special sales promotion by the manufacturer. She secured a loan from the manufacturer in the amount of $21,000 at a rate of 8% / year compounded monthly. Her bank is now charging 11.1% / year compounded monthly for new car loans. Assuming that each loan would be amortized by 36 equal monthly installments, determine the amount of interest she would have paid at the end of 3 yr for each loan. How much less will she have paid in interest payments over the life of the loan by borrowing from the manufacturer instead of her bank? (Round your answers to the nearest cent. interest paid to manufacturer $_____ interest paid to bank saving$____ savings$______

The sales tax rate for the state of Washington was 9.3%. What is the sales tax on a $4,400 car in Washington? $__ What is the final cost of a $4,400 car in Washington, including tax? $__ Round your answers to the nearest cent as needed.

You want to put a 3 inch thick layer of topsoil for a new 25 ft by 29 ft garden. The dirt store sells by the cubic yard. How many cubic yards will you need to order? You need to order cubic yards of topsoil.

Three planes are defined as follows: -7x+ -2y+ -7z+ 30 = 0 -6x+ -5y + -10z + 0 = 0 -10x+ 6y + -7z+ 24 = 0 Determine how these planes intersect. If they intersect in a line, let your answer be the z- coordinate of the direction vector. If they do not intersect, write "NULL". If they intersect in a plane, write "coincident". If they intersect at a point, provide the z-coordinate of the point.

Problem22. Triangle OAB has O = (0,0), B = (4, 0) and A in the first quadrant. In addition, ZABO = 90° and ZAOB = 60° . Suppose that OA is rotated 90° counterclockwise about O. What are the coordinates of the image of A? (A)(4√3,4) (B)(-4√3,4) (D)(√3,4) (C) (4√3,-4) (E)(-√3,4)

Indicate whether the following process will result in a vector or scalar quantity. If neither vector or scalar, choose meaningless. A. (ū − v) × (ū + v) B. (2u-v) (u.v). C. (Proj, (2u-v)-u).v D. (2-0) xu E. v. (uxu)-3/w u.v

Find ||u||, ||v||, and ||u + v|| u=(-3, ½)₁ x = (4, - 1/4 ) (a) ||u|| (b) ||v|| (c) ||u+v||

Given v = 4i and w = 2i + 5j, find the angle between v and w.

Obtain a vector v by rotating the vector u= 2 by 135° in the counter-clockwise direction. -1

Given v = 21-j and w=8i + 3j, find the angle between v and w.

Use the given vectors to find vw and v.v. v=-81-4j, w = -9i - 6j

Find the magnitude ||v|| and the direction angle θ for the given vector v. v = -7i+ 12j

Consider two vectors υ = (-3,2,-1) and ν= (1, -3, 2), evaluate the following: a) (A:1)υ.ν b) (A:1) Angle between υ and ν c) (A:2) υ×ν d) (A:2)Projᵥυ e) (A:1)Area of parallelogram produced by υ and ν. f) (K:1, Ⅰ:1) if ω= (3, 4, 2), are υ,ν and ω linearly dependent or independent? If they are not, calculate the volume of the parallelepiped these three vector form. g) (1:2, A:2) Can p = (2, 5, -3) be written as linear combination of υ,ν and ω? If so, state the correct linear combination. If not, explain why not.

Find lul, lvl, |1/2vl, lu+vl, lu-vl, and lul - vl. u = 4i + j, v = 5i - 2j

Consider the following. U= (4,0), v= (7,9) (a) Find u. v. u v = (b) Find the angle between u and v to the nearest degree. θ =

Find u - v, 2(u + 3v), and 2v - u. u = (6, -2, 7, 3), v = (-2,2/3,-7/3,-1) (a) u-v= (b) 2(u + 3v) = (c) 2v - u =

Explain what a linear transformation is from the algebraic and geometric, showing the relationship between them.

Theorem 114. If a dilation has scaling factor 3, then the length of every segment PQ is multiplied by 3, that is, L(P'Q') = 3L (PQ). In the same way, we can show that distances are proportional under every positive rational scaling factor. Through a calculus type limit

Let v₁ = [1 -1] and v₂ = [3 -2].be two vectors in R². (a) Determine whether v = [2 2] belongs to span{v₁, v₂} (b) Determine whether {v₁, v₂} are linearly independent

I have a class of 30 students. I can select a group of 4 students to present as a group, or I can choose 4 students to present one at a time. How many possible groups are there versus how many sequences of individual presentations?

Prove that if a surface Σ is diffeomorphic to the torus, then ∫ΣKdA = 0.

Prove that if a surface ∑ is diffeomorphic to the torus, then ʃ∑ KdA=0.

Let A ∈ Rᵐ*ⁿ with A² - 4A +3In, = O (where O is the n x n zero matrix). (a) Show that A is invertible. (b) Find all possible eigenvalues of A.

A matrix with only one column and no rows is called Select one: a. Zero matrix b. Identity matrix c. Raw vector matrix d. Column vector matrix

Given points A(2; 2; -1), B(3; -1;1), C(4;1;2), D(1; -1; 1). Find... 1. Scalar product of vectors AB and AC 2. Angle between the vectors AB and AC 3. Vector product of the vectors AB and AC 4. Area of the triangle ABC

Vector u = PQ has initial point P (3, 17) and terminal point Q (9, 2). Vector v = RS has initial point R (30, 6) and terminal point S (8, 18). Part A: Write u and v in linear form. Show all necessary work. Part B: Write u and v in trigonometric form. Show all necessary work. Part C: Find 7u - 4v. Show all necessary calculations.

You write each of the 26 letters of the alphabet on separate index cards. Part A; If you choose 3 cards at random without replacing them, what is the probability of choosing A, B, and C? Part B; If you choose 2 cards at random without replacing them, what is the probability that you will not draw an A?

Let A be an invertible matrix and λ be an eigenvalue of A. Prove, using the definition of an eigenvalue, that is 1/ λ an eigenvalue of A-¹. If A is an invertible matrix that is diagonalisable, prove that A-¹ is diagonalisable.

Jordan and 4 of his friends are are riding in a car. What is the probability that Jordan is in the front passenger seat? 1/120 2/5 1/5 1/10

Graph the circle x² + y² = 4. Plot the center. Then plot a point on the circle. If you make a mistake, you can erase your circle by moving the second point onto the first.

Solve using the quadratic formula. 5t² +8t=0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. t or t=

Solve using the quadratic formula. -(3q²) - (7q) = 0.Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. q= __ or q= __

Example: The diagram shows a cuboid whose vertices are Q. A, B, C, D, E, F and G. Vectors a, b and c are the position vectors of the vertices A, B and C respectively. The points and w and x the points Y and Z lie on OA and EF such that OW: WX :XA = 1:3:1=EY: YZ: ZF. Prove that the diagonals WY and XZ bisect each other.

To be able to: Use vectors to solve generalised geometric problems Vectors are often used to prove general properties about geometric arrangements. In the following examples, no coordinates or specific vectors will be given. We often make use of the following fact: In n dimensions, each vector is a unique linear combination of a non-parallel vectors. Example: OABC is a parallelogram. The vectors ar and e are the position vectors of points 4 and C respectively. Prove that the diagonals of OABC bisect each other. Method 1 Let point P be the intersection of the diagonals AC and OB Method 2 Let points P and Q be the mid-points of AC and OB respectively.

Let L₁ be the line passing through the point P₁=(-1, 0, 6) with direction vector d₁[-1-3,-1, 1]ᵗ, and let L₂ be the line passing through the point P₂=(7, 3, 11) with direction vector d₂[-3, -5.-3] ᵗ. Find the shortest distance d between these two lines, and find a point Q₁ on I₁., and a point Q₂ on L₂ so that d(Q₁,Q2)=d. Use the square root symbol 'v' where needed to give an exact value for your answer. d = 0 Q1= Q2=

A class consists of 60 % men and 40% women. Blond men compose 25% of the class, and blond women make up 20% of the class. If a student is chosen at random and is found to be a male, what is the probability that the student is blond? A 0.34 B. 0.42 C. 0.54 D. 0.63