True or False and explain 1- For any two non parallel and non orthogonal vectors a and b with angle θ between them, it holds that cosθ(a.b) = sinθ(axb). 2- If r(t)=⟨−4cos(2t),3sin(3t),ln(2t)⟩, then the ∫r(t)dt is equal to ⟨−2sin(2t),−cos(3t),tlnt−t⟩+C, where C is a vector constant of integration.

True or False and explain 1- For any two non parallel and non orthogonal vectors a and b with angle θ between them, it holds that cosθ(a.b) = sinθ(axb). 2- If r(t)=⟨−4cos(2t),3sin(3t),ln(2t)⟩, then the ∫r(t)dt is equal to ⟨−2sin(2t),−cos(3t),tlnt−t⟩+C, where C is a vector constant of integration.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 34E

See similar textbooks

Related questions

Q: Please do problem 2. Thank you!

Q: a. Zadia placed $800 in a savings account which pays 6% interest compounded annually. At the end of…

A: Zadia invested in a savings account which pays interest compounded annually.The aim is to find the…

Q: If A is a subset of universe , find each of the following AUU= B. C

A: Let us solve above problem

Q: Make a sketch of the given function on [0, ∞) and express it in terms of the unit step function: a)…

Q: Find the standard matrix of the linear mapping L ab sin (a) f Əx ∞ α 52 5 2 x2 23. [2271²-1472²7223]

Q: Elvaluate dz around the unit circle with greater than unity?

Q: If A(cos a, sin a), B(sin a, -cos a), C(1, 2) are the vertices of AABC, then as a varies, find the…

Q: The point x = 0 is a regular singular point of the differential equation. 1 x²y" + (²x + x²)x¹. y -y…

Q: The iterated integral (fr Cos[0], r Sin[0]]r do) dr equals the 2D area-weighted integral f(x, y] da…

A: Given iterated integral .We have to find the domain for

Q: an = 2 an-1 + 8 an-2; ao =4, a₁ = 14 The closed form solution is: an = n+

Q: pays a fixed amount for water, electricity, security and a loan of TTD100.00, TTD1,200.00,…

A: Since you have posted a multi subparts question according to guidelines I will solve…

Q: Use an integral to find the area of the surface parameterized by r(u, v) = (u cos v, u sin v, u²), u…

A: The surface parameterized by ,…

Q: 4. Prove that (m) is even for all m > 3.

Q: Let K be a finite normal extension of a field F. If a, ß are any two elements of K c onjugate over…

A: Let be a finite normal extension of a finite field Suppose that are any two elements of conguate…

Q: An oil company processes oil into aviation fuel and heating oil. It costs $65,000 to purchase each…

A: Given information:An oil company purchases barrels of oil for .Distillation of barrels of oil…

Q: It is not always possible to construct by ruler and compass, a square equal in area to the area of a…

A: We have to check that 'it is not always possible to construct by ruler and compass, a square equal…

Q: In(x) - 6x² In(x) = -5 ln(x)

A: Given that the equation is:

Q: Solve the following linear programming problem by applying the simplex method to the dual problem.…

Q: The necessary and sufficient condition for a non to be a subspace of V is a - empty subset W of a…

A: To prove that the necessary and sufficient condition for a non-empty subset of a vector space to…

Q: Given each of the following: a) Identify the critical numbers of the function classify each as a…

Q: 63-76. Concavity Determine the intervals on which the following functions are concave up or concave…

A: Note:As per our guidelines, we can solve first question. Please repost the remaining questions.

Q: lim,... sin(7) does not exist. 2

Q: 3. A password is a sequence of letters (a-z) and digits (0-9). Find the number of passwords of…

A: Given that the number of letters (a-z) and the digits (0-9) is used to form a password of length…

Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system. (-15) x +…

Q: : Mark all the ODEs in the list for which the function y(t) = cos(t) is a solution. A) y' = sin(t)…

Q: 1. Use the extended Newton divided difference method to obtain a quartic polynomial that takes these…

Q: If y, and y2 are linearly independent solutions of t2y" + 3y +(4+t)y = 0 and if W(y₁, y2)(1) = 3,…

A: Given y1 and y2 are linearly independent solutions oft2y" + 3y' + (4+t)y = 0 Also, , where is…

Q: lim,** 3 5n-2 0

A: Since you have posted a multiple question according to guidelines I will solve first question for…

Q: Exercise 8.1.5 Let A = 24 -4 -1 6-9 00 -3 This matrix has eigenvalues λ = -3 and 2 = 4. Find a basis…

Q: Let D be the circle |z| = 3, oriented counterclockwise. For any positive integer n compute the…

Q: 1. Consider the matrices 0 4₁-(13), 1 3)₁ 4₂2 - ( -8 -2) ₁4₁ = (3-2). 0 1 3 -5 -4 A₁-(3) -4 0 and A4…

A: We have to match the given matrix with the function represented in the graph

Q: 1. A company needs to locate a distribution facility somewhere between the source of raw materials…

A: Given information:The company needs to locate a distribution facility between the source of raw…

Q: 14. ERROR ANALYSIS Describe and correct the error in determining whether AJKL = ALMJ. X M JL = JL…

A: The hypotenuse-leg (HL) theorem states that if the hypotenuse and a leg of a right triangle are each…

Q: Calculate the double integral LL costs 1² by changing the order of integration. cos(√³)dxdy

A: Given

Q: A square matrix A is invertible if and only if det A + 0. Use the theorem above to find all values…

Q: Consider the function f(x)=2x-3 4 find its inverse and draw its graph

Q: Solve, using the Chinese method of solving higher degree polynomial equations: x³ + 15x² +27x =…

Q: Find the absolute maximum and minimum values of f on the set D where f(x, y) = x² + 4y² - 2x − 8y +…

Q: Compute the determinant using cofactor expansion along the first row and along the first column. 102…

A: Given: We have to complute the determinant using cofactor expansion along the first row and along…

Q: 10. Use induction to show that 1x2 + 2x3 + + n(n+1) = " for all n € N.

Q: Toys Toys Toys, a small producer of collectors' toys, is attempting to determine the value of one of…

Q: Assume the company makes a profit of $15 per bookshelf and $40 per desk. They must manufacture…

A: The company makes a profit of per book self and per desk.The manufacturer must make book self in…

Q: 3.6. Consider IR3 with the inner product :=x T210 1 2 -1 (0-12√y. (S) Furthermore, we define ez,…

A: Consider with inner product:.We need to find orthogonal projection and distance.

Q: Make a change of variable, x = Py, that transforms the given quadratic form into a quadratic form…

A: The given quadratic form is The matrix of the above…

Q: The third term of a geometric progression is the same value as the fourth term of an arithmetic…

A: The nth term of a geometric sequence is where a is the first term and r is the common ratio.The nth…

Q: Which of the four equations A)-D) has a solution that satisfies the equation y² – t² = 1?

A: We have, d/dt (t^n) =n t^(n-1)

Q: Example: Let R = {(u, v)|1 ≤ u ≤ 2,2 ≤ v ≤ 4} be the region S trans- formed by T(u, v) = (u², u +…

Q: Find the inverse Laplace transform L¯¹{F(s)} of the function F(s) L-¹{F(s)} = = 6 (s − 1)³ NOTE: The…

Q: 4.6.A Let A be a m x n matrix. What is the largest possible dimension of (a) the null space of A?…

Q: Introduce slack variables as necessary, then write the problem. Maximize subject to: with Complete…

Question

True or False and explain

1- For any two non parallel and non orthogonal vectors a and b with angle θ between them, it holds that cosθ(a.b) = sinθ(axb).

2- If
r(t)=⟨−4cos(2t),3sin(3t),ln(2t)⟩,
then the ∫r(t)dt is equal to
⟨−2sin(2t),−cos(3t),tlnt−t⟩+C,
where C is a vector constant of integration.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution