Vector Calculus Resources

Please show me the details step. I am the beginner

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...

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⇀...

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...

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)}

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...

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...

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...