need Explanation Step by step on paper.,I already wasted one question and this is my last, need its detailed explanation with correct answers on paper.I have the Final answers just need Explanation so i can understand, Please don't waste my time and money let the expert person do thia, i have already reported a guy for giving me wrong answer.

1) Given the below four points in space, verify that they are the vertices of a parallelogram 50 pts each and find the area Choose one of the below. (0, 0, 0) (3, 2, 4) (5, 1, 4) (2, -1,0) 1) Find the volume of the region below the plane 3x + y + z = 3 and above the xy plane in 2) Given the below four points in space, verify that they are coplanar or find the area of the the first octant. You may use either a double integral or a triple integral. parallelpiped formed by the vectors between the points. (0, 1, 2) (2, 0,1) (1, -1, 1) (-1, -1,0) 2) Use a triple integral to find the volume of the region under the plane 6x + 8y + z = 12 in the first octant. 3) Prove that the cross product of any vector with itself yields 0. You may not simply 3) Convert to cylindrical coordinates and evaluate. choose random numbers for vector components - you must perform the proof in symbol form. I'll x dz dy dx 4) Convert to spherical coordinates and evaluate. V x z + yz + z' dz dy dx 1) Let r(t) = (2t, 6 - t2). Find v(t) and a(t) at the point (2,5). 2) Find unit tangent vector T(t) at the point (6V2, 6V/2,3) to r(t) = (12 cost, 12 sin t, 3). Let u = (4,14, -2) v = (-5,2,4) w = (2,0, -5) be vectors in space. 3) Find principal unit normal vector N(t) att = = to r(t) = (5 cost,5 sint). 1) Find the angle between the x-axis and u 10 pts 4) Find normal component of acceleration an(t) at t = = to r(t) = (4 cost, 4 sin t, 5t). 5) Find tangential component of acceleration aT(t) att = 2 to r(t) = (6t - 7,t2, -10). 2) Find the angle between the y-axis and u 10 pts Round your answer to four decimal places. 6) Find the length of the curve given by r(t) = (2t, 5 cost , 5 sint) on [0,3]. 7) Find curvature Kofr(t) = (t, 2t2, 2t). 3) Find the angle between the z-axis and v 10 pts 4) Find projuw 10 pts