Question: The helix r(t) = (cos(t/2), sin(t/2), t) intersects the sphere x 2 + y 2 + z 2 = 2 in two points. Find the

The helix r(t) = (cos(πt/2), sin(πt/2), t) intersects the sphere x2 + y2 + z2 = 2 in two points. Find the angle of intersection at each point.

Step by Step Solution

★★★★★

3.44 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Parametric equations for the helix are x cosnt2 y sint2 z t and substituting into the equation of th... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

The intersection of the plane y = 1 with the sphere x2 + y2 + z2 = 1 Find a parametrization of the curve

Q:

Let G be the sphere x2 + y2 + z2 = a2. Evaluate each of the following: (a) (b) (c) (d) (e) Use symmetry properties to make this a trivial problem? z dS y, x + + sin z 1 + z dS x dS (r2 y) ds

Q:

The sphere x2 + y2 + z2 = a2 has constant area density k. Find each moment of inertia? (a) About a diameter (b) About a tangent line (Assume the Parallel Axis Theorem from Problem 28 of Section 13.5)

Q:

1. (1 point) Find an example of u, v, w E R* to show that the cross product is not associative (i.e., find an instance where (u x v) x w / ux (v x w)). 2. (6 points) (a) Find an equation of the plane...

Q:

MATH 108 Quiz 3 Name Click here to enter text. This quiz is worth 40 points. Questions 1 - 4 are each worth 4 points; do not show your work. Questions 5 - 8 are each worth 6 points; show your work to...

Q:

MA 261 PRACTICE PROBLEMS 1. If the line ` has symmetric equations y x1 z+2 2 = 3 = 7 , nd a vector equation for the line `0 that contains the point (2; 1; 3) and is parallel to `. A. ~ = (1 + 2t)~...

Q:

14.1 SUMMARY . A vector-valued function is a function of the form A sample is shown fort cate with a diagram the position vectors r ( t ) = (x (1 ) . y (1), z(1) > = x(1)i + >(1)j+ z(1)k (10 - DZ + 1...

Q:

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

Q:

1. 3 2 Consider the function f(x) = x - 3x - 9x + 10, x (a) . Find the equation of the straight line passing through the maximum and minimum points of the graph y = f(x). (4) (b) Show that the point...

Q:

Chapter Thirteen A FUNDAMENTAL TOOL: VECTORS Contents 13.1 Displacement Vectors . . . . . . . . . . . . 686 Notation and Terminology . . . . . . 686 Addition and Subtraction of Displacement Vectors ....

Q:

Using data set E, answer the questions given below. DATA SET E Microprocessor Speed (MHz) and Power Dissipation (watts) (n = 14 chips) Speed (MHz) Chip 1989 Intel 88486 Power (watts) 20 1993 Pentium...

Q:

A and B were partners in a firm sharing profits and losses in the ratio of 3:2. They admitted C as a new partner for 3/7th share in the profit and new profit sharing ratio will be 2: 2:3. C brought...

Q:

If the yield curve is upward sloping: A . investors expect the short - term interest rates to fall in the future. B . investors often shift their investment holdings away from long - term securities...

Q:

How should we decide to allocate nonrenewable resources across different generations?

Q:

The function f has a root of multiplicity 2 at r if f(r) = f'(r) = 0 and f"(r) 0. In this case, a slight modification of Newtons method, known as the modified (or accelerated) Newtons method, is...

Q:

Evaluate the following limits lim x csc X |x0

Q:

Evaluate the following limits. Use lHpitals Rule when needed. In y lim y0* Vy

Q:

true and false. please answer all questions Word or Phrase Cost Behavior Analysis Cost Volume Analysis Description The study of how specific cossts respond to changes in the leverl of business...

Q:

Working Capital Cash Flow Cycle Strickler Technology is considering changes in its working capital policies to improve its cash flow cycle. Strickler's sales last year were $120,000 (all on credit),...

Q:

how many multiplexers are there in the bus?