44 Answered Questions for the topic Vector Calculus

Vector Calculus Calculus Calc Vector


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

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


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


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


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.
Vector Calculus Calculus Integral Calculus


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=... more


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... more
Vector Calculus Calculus Theorems Vectors


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


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 Calculus Calculus College


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

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


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

Please show to the details step
Vector Calculus Precalculus Math Help Math Tutor


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


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
Vector Calculus Maths Sets Vector


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
Vector Calculus


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
Vector Calculus


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
Vector Calculus


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
Vector Calculus


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


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)
Vector Calculus Calculus Calculus 3


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 = <?, ?, ?>
Vector Calculus Calculus Calculus 3


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)|= ?
Vector Calculus Calculus Precalculus Vectors


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. 
Vector Calculus Math Calculus Math Problem


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


Are linearly dependent vectors always coplanar?

If not, when would linear dependency imply coplanarity?

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