Question

Find a vector parallel to the plane 2x - y - z = 4 and orthogonal to i + j + k

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Other

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Define the cross product (vector product) of two vectors. Which algebraic laws are satisfied by cros...

A: Cross product of vectors a and b is vector c which is perpendicular to both and b , with direction g...

Q: What are Taylor polynomials? Of what use are they?

A: Let us take a function f, a specific point x = a (called the center), and a positive integer n, the ...

Q: #9

A: Given:Initially water tank holds 300 gallons of water.Rate at which the pure water is pumped into th...

Q: #1

A: Given differential equation and its solution is

Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope ...

A: We first have to find the slope of the given vector and the line. If the slopes are equal then they ...

Q: Under what conditions can you find the area of the surface gener-ated by revolving a curve x = ƒ(t),...

A: Click to see the answer

Q: Find the vertex, focus, and directrix of the parabola x2 - 6x - 12y + 9 = 0.

A: Write the given parabola in standard form by completing square

Q: Let y be the percent increase in annual US national production during a year when the unemployment r...

A: a) If we plug u=0 in y=3.5-2u then we get y=3.5 .u=0 means no change in the unemployment rate.So 3.5...

Q: Find the area under y = x^3 over [0, 1] using the following parametrizations. a. x = t^2, y = t^6 b....

A: Click to see the answer

Q: Exercises 49–50 give equations for ellipses and tell how many units up or down and to the right or l...

A: Note: We’ll answer the 49th question since we answer only one question at a time. Please submit a ne...

Q: #13

A: Given,

Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8 interse...

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become: 

Q: 3. Write the function defined by fx) = -2x2- 12x in vertex form and identify the vertex of the parab...

A: Given,

Q: Find a 2 * 2 determinant formula for the area of the triangle in the xy-plane with vertices at (0, 0...

A: Given, vertices of the triangle are

Q: If vector AB = i + 4j - 2k and B is the point (5, 1, 3), find A.

A: Given,

Q: I need to compute each limit. The limit is ... lim x -> -3 x2 + x - 6 ————— x3 + 27

A: Given,

Q: Find the center C and the radius a for the spheres in Exercises 51–52. 51. x2 + y2 + z2 - 6y + 8z = ...

A: We’ll answer the 51th question since we answer only one question at a time. Please submit a new ques...

Q: Exercises 39–42,  find an equation for the line through P parallel to v. Then sketch the line. Inclu...

A: Since we only answer up to 1 question, we’ll answer the first question. Please resubmit the question...

Q: 4x² + 5 -dx 3

A: Given, integral is

Q: Find the volume V of the described solid S. A right circular cone with height 7h and base radius 4r ...

A: Given that height of right circular cone is 7h and the base radius is 4r.

Q: Find the first four nonzero terms in the Maclaurin series for the functions in Exercises 31–38. 31. ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: What is the determinant formula for calculating the cross product of two vectors relative to the Car...

A: Consider two vectors relative to the Cartesian i, j, k-coordinate system.

Q: In Exercises 1–2, find the length and direction (when defined) of u * v and v * u. 1. u =-8i - 2j - ...

A: find the length and direction (when defined) of u * v and v * u.

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) 6x2 + x – 1 lim x...

A: Given, limit function is

Q: In the function:  f(x)= (7x+B)/(4x+b) , with 7b>4B When is the function increasing and when is th...

A: Function is increasing where slope f’(x) >0 and decreasing where f’(x) <0. Find the derivative...

Q: The line segment joining the points (0, 1) and (2, 2) is revolved about the x-axis to generate a fru...

A: To determine the surface area of the frustum.

Q: Find the volume of the solid generated by revolving the region enclosed by the ellipse 9x2 + 4y2 = 3...

A: Find the volume of the solid generated by revolving the region enclosed by the ellipse 9x2 + 4y2 = 3...

Q: Find the derivative of the following function and evaluate the derivative at the given value of x. f...

A: The given function is,

Q: Find an equation for the plane that passes through the point (-1, 6, 0) perpendicular to the line x ...

A: Direction ratios of line x =-1 + t, y = 6 - 2t, z = 3t are  <1,-2,3> .Sine line is perpendicul...

Q: f(x) =sqrt16 − x2, g(x) =sqrt x + 2 Find (f + g)(x).

A: Given,

Q: In Exercises 1–8, find the eccentricity of the ellipse. Then find and graph the ellipse’s foci and d...

A: Click to see the answer

Q: Sketch the surfaces 1. . z = x2 + 4y2  2. x = 4 - 4y2 - z2 3. x2 + y2 = z2

A: The given surfaces are sketched using online 3D calculator.

Q: What is a hyperbola? What are the Cartesian equations for hy-perbolas centered at the origin with fo...

A: Problem 1:Recall the following fact.

Q: Suppose that A, B, and C are vertices of a triangle and that a, b, and c are, respectively, the midp...

A: Let A=(x1,y1,z1)B=(x2,y2,z2)C=(x3,y3,z3) 

Q: In Exercises 35–38,  find an equation for the line through P perpendicular to v. Then sketch the lin...

A: given an equation for the line through P perpendicular to v

Q: In Exercises 33 and 34, find the distance from the point to the plane. 33. (6, 0, -6), x - y = 4 34....

A: We know that distance of point  (x1,y1,z1) from plane ax+by+cz+d=0 is given by

Q: How do you find equations for spheres in space? Give examples.

A: How to find equation of spheres in space? Give example

Q: What theorem sometimes enables us to use l’Hôpital’s Rule to calculate the limit of a sequence? Give...

A: The theorem which enables us to use L'Hospital’s Rule  is,

Q: Find all real zeros of the function. g(x)=5(x2-36)(x-7)(x+7)2

A: Click to see the answer

Q: if you have a parametric equation grapher, graph the equations over the given intervals  a. Epicyclo...

A: a) Graphed Epicycloid x = 9 cos t - cos 9t, y = 9 sin t - sin 9t; 0<=t<=2pai using graphing ca...

Q: In Exercises 17 and 18, find |v| , |u| , v .u, u. v, v * u, u * v, |v * u| , the angle between v and...

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any s...

Q: Find the point on the sphere x2 + (y - 3)2 + (z + 5)2 = 4 nearest a. the xy-plane. b. the point (0, ...

A: Consider the given equation of the sphere.

Q: In Exercises 1–3, find a. v. u,| v|,|u| b. the cosine of the angle between v and u c. the scalar com...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: Find the volume swept out by revolving the region bounded by the y-axis and the graph of x = t (1 - ...

A: Given,

Q: find the Taylor series at x = 0 of the functions in Exercises 1–2. 1.ln(3+6x) 2. 5sin ( -x)

A: Consider the given question,(1)The Taylor series at x = 0 is given by,

Q: Estimate the error if P 3(x) = x - (x^3/6) is used to estimate the value of sin x at x = 0.1.

A: Given:

Q: Exercises 53–54 give equations for hyperbolas and tell how many units up or down and to the right or...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Find Taylor series at x = 0 for the functions  1/1 - 2x

A: The Taylor series expansion of a function f(x) at the point x = a can be written as

Q: For what value or values of a will the vectors u = 2i + 4j - 5k and v = -4i - 8j + ak be parallel?

A: Given,

Q: Exercise 2: Determine the average value of the following functions, on the given interval. (a) x³, o...

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question...