Compute the volume of the parallelepiped with vertices (0,0,0) (0,1,0) (1,1,0) (1,2,0) (1,1,1) (1,2,1) (2,2,1) (2,3,1)

Please show me the details step. I am the beginner 

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

Please show to the details step

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 form...

r = A (cos t - sin t) i + A (cos t + sin t) j + Bt k . Find A B given P(10,10,0), Q(0,10sqrt(2), 3/4pi)

note that I,j,k & r is a vector form

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...

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 ∈ A I...

Vector Problem

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

I need help solving this vector problem

If the triangle ABC has vertex C located at point C=(2,−6,−1) and vertex A located at point A=(−1,−2,5), and if side AB has the same length as side CA, and is in the direction of the vector v⇀...

Vector calculus Lagrange multipliers question

Assume you are given the surface S with equation x^2+y^2/9+z^2/4=1   (a) Find the equation of the tangent plane to S at the point (√3/6, √6, 1). (b) Find a point on the...

Assume you are given the surface S with equation x^2+y^2/9+z^2/4-1

Give an equation for and geometrically describe the set of points on S so that the tangent plane to S at those points contains the point (3,0,0).   The correct answer is 6x-18=0...

determine whether the vector (-4, -9, 2, -1) is in the subspace v=span{( 1, 3, -2, 1), ( -3, -9, 6, -3), (2, 5, -2, 1), (3, 8, -4, 2)}

determine whether the vector (-4, -9, 2, -1) is in the subspace v=span{( 1, 3, -2, 1), ( -3, -9, 6, -3), (2, 5, -2, 1), (3, 8, -4, 2)}

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...

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...

find the orthogonal projections of b onto a

Let a = (-8, 9, 9) and b = (2, 1, 8) be vectors. Find the orthogonal projections of b onto a   I've found the scalar and vector projection but i couldn't find Orthogonal Projection   Also what...

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?

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)

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 = <?, ?, ?>

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) = <?, ?, ?>...

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. 

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...