44 Answered Questions for the topic Vector Calculus

#### What is the slope of the line 𝜃=(1/8)pi?

(Use decimal notation. Give your answer to three decimal places.)

#### Find the second and the third components of a vector 𝐧 normal to the plane with the equation 12𝑥+9𝑦−8𝑧=3 if the first component of the vector 𝐧 is equal to 12.

(Give your answers as a whole or exact number)

#### Find the equation of the line that passes through the point (7,3,4) and is perpendicular to the plane −9𝑥+2𝑦+10𝑧+6=0.

(Use symbolic notation and fractions where needed. Give your answer as a list in the form where the equation of the line is

Vector Calculus

12/01/20

#### vector calculus in mathematics

A boat travels due West with a speed of 30 mph. If there is a 7 mph current at North 30 degree West, find the actual speed and direction of the boat.1

Vector Calculus

09/25/20

#### I'm struggling to understand this problem. It seems that the location of the points of the cube don't match up to make a cube.

Find an equation of the largest sphere contained in the cube determined by the planes x = 2, x = 16; y = 4, y = 18; and z = 7, z = 21.

02/12/20

#### Calculus: Vector Integration

Three paths from (0,0) to (1,2) are defined by (a) y=2x (b) y=2x^2(c) y=0 from (0,0) to (1,0) and x= 1 from (1,0) to (1,2). Sketch each path and along each path find (integral)c Fdr, where F=...
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01/11/20

#### Projectile Motion using Vector Calculus

Trebuchet can throw an 80 lb rock up to 100 yards. The maximum height that the rock reaches as it flies through the air toward a fortress wall 100 yards away is 20 yards, calculate the initial...
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#### 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...
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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

#### 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

Vector Calculus

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...
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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...
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#### 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...
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Vector Calculus

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) =...
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Vector Calculus

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...
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Vector Calculus

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...
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Vector Calculus

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?

Vector Calculus

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...
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06/29/17

#### Are linearly dependent vectors always coplanar?

If not, when would linear dependency imply coplanarity?

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