37 Answered Questions for the topic Vector Calculus

Verification of Stokes Theorem

Could someone explain how do we verify stokes theorem for the vector field F=zi + (2x+z)j + xk taken over the triangular surface S in the plane (x/1)+(y/2)+(z/3)=1 bounded by the planes x=0 y=0 and... more

10/26/19

Vector Calculus

How do we evaluate the volume under the surface given by, z=2xsin(y) over the region bounded below by the curve y=x^2 and above by the line y=0 for 0<=x<=1

10/25/19

Vector - Scalar Potential

Vector a = (6xy + z^3)i + (3x^2 - z)j + (3xz^2 - y)k Find the scalar potential Q that vector a =grad Q

10/19/19

Vectors - lines and equations

1) How do we find the perpendicular distance of a point C=c fron the straight line (r-a)^b =02) how do we find the shortest distance between the two skew lines (r-a)^b =0 and (r-c)^d =0

09/15/18

Find a unit vector in the xy plane that is perpendicular to a=3i-5j+k

Please show to the details step

06/19/18

Vector u has its initial point at (21, 12) and its terminal point at (19, -8).

Vector u has its initial point at (21, 12) and its terminal point at (19, -8). Vector v has a direction opposite that of u, whose magnitude is five times the magnitude of v. Which is the correct... more

04/10/18

if a, b, c, and r are any vector, prove [a.bxc]r = (a.r)bxc + (b.r)cxa + (c.r)axb

Im using a period as dot product and x for cross product. I've been stuck on this problem for a long time. My main question is, if there is a vector next to a parenthesis does that imply cross or... more

03/07/18

A question on convex sets

The definition I’ve been given of convex inequalities is the following:A set A ⊂ Rn is convex if:• For any vectors a, b ∈ A• For any λ ∈ [0,1]• The point λa + (1 - λ)b ∈ AI don’t know what the λ... more

01/23/18

Vector Problem

If the vector (−6,−9) is multiplied by 5 and thentranslated so its tail is at the point A = (2,−9),find the coordinates of its head.   I understand that to multiply the vector you do: 5(-6,-9) =... more

10/30/17

Find the flux given the field.

A magnetic field is given by B(x,y,z) = C(xi + yj − 2zk) where C is a constant. Find the flux of B across the surface of a square coil of side length a when it is placed a distance 2a from the... more

10/24/17

Find the path C such that C(0)=(-3,-1,4) and C't=(6t, e^(6t), t^3)

I know x=3t^2-3, and z=(t/4)^4+4. But I don't know how to find y. The correct answer of y is e^6t/6 - 7/6. How to get it? I stop in the step (1/6) e^6t+C.   How to get the C? How to find the anti... more

10/20/17

What is the angle in radians between the vectors

What is the angle in radians between the vectors?   a= (-2, -2, 3) and b = (-4, 0, 7)   angle?

10/20/17

find a.b if a=(-1, 5, 5) and b= (-6, 8, 7)

find a.b if a=(-1, 5, 5) and b= (-6, 8, 7)

09/11/17

Find two unit vectors orthogonal to a = <4,-1, 2> and b = <3, 3, 1>

Find two unit vectors orthogonal to a = <4,-1, 2> and b = <3, 3, 1>   First vector = <?, ?, ?> Second vector = <?, ?, ?>

09/11/17

Find the velocity, acceleration, and speed of a particle with position function

Find the velocity, acceleration, and speed of a particle with position function r(t) = <-7tsin(t), -7tcos(t), 4t^2>   v(t) = <?, ?, ?> a(t) = <?, ?, ?> |v(t)|= ?

08/27/17

Find the vector(s) v satisfying the given conditions. u={5,4}, u*v=2, |v|^2=13

The answer needs to be simplified and written in the form of ai+bj. 

08/26/17

Calculus III Question

A weight of 100 pounds is suspended by two ropes A and B. Rope A makes an angle of 30 degrees with the ceiling and rope B makes an angle of 45 degrees with the ceiling. What are the magnitudes of... more

06/29/17

Are linearly dependent vectors always coplanar?

If not, when would linear dependency imply coplanarity?

06/25/17

MY QUESTION IS VERY DETAIL PLEASE CHECK DISCRIBTION

you are on a boat 400 m from the closest point Perpendicular on the beach. you want to visit your friend who is located another 1km along the beach. if you can row pedal boat at a constant speed of... more

03/30/17

Lagrange Multipliers

Find all of the extrema of g(x,y,z)=xyz on the surface z=e^(-x^2-y^2).

03/12/17

Vector Fields

For each vector field in R4 given below, either find a function for which it is the gradient, or explain why no such function exists. Variables are in the order x, y, z, w. a.(siny + wcosx + 1)e1 +... more

12/15/16

Vector physics help!

Suppose a body has a force of 10 pounds acting on it to the right, 25 pounds acting on it -135° from the horizontal, and 5 pounds acting on it directed 150° from the horizontal. What single force... more

12/15/16

If vector v has an initial point and a terminal point write v as multiples of the basis vectors, write v in the form v = ai + bj.

If vector v has an initial point at P1 and a terminal point at P2, write v as multiples of the basis vectors i = <1,0> and j = <0,1> That is, write v in the form v = ai + bj.   P1 =... more

12/15/16

Find a unit vector that points in the opposite direction as v.

Find a unit vector that points in the opposite direction as v.   Let .v=-3(pi 2)i-4(pi 2)j   A. u= (3/5)i+(4/5)j B. u= -(3/5)i-(4/5)j C. u= -(5/3)i-(5/4)j D. u= (5/3)i+(5/4)j  

12/04/16

Vector5.13

Find a unit vector in the direction of the vector v=〈√2,√2〉.   Please show step by step work to solution and provide final answer. Please and Thank You!
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