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Find the equation of the tangent place to surface trace by the parametric function given below, to the point (1, 0, 5).
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- Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a orthocenter? b centroid?A particle is acted upon by constant forces 4i+j-3k and 3i+j-k and is displaced from the point (1,2,3)to the point (5,4,1). Find the total work spent by the forces ?Find the distance between u = (-1,2,5) and v = (3,0,1)
- The vector between the origin (0, 0, 0, 1) and the point (x, y, z, 1) is the difference v = __ . In homogeneous coordinates, vectors end in So we add a __ to a point, not a point to a point.1. Solve by Cramer’s rule 3x + y + 4z = 11 4x – 4y + 6z = 11 6x – 6y = 3 2. Find the volume of tetrahedron given the following (1, 0, 1), (0, 1, 0), (0, 0, 1), and (1, 1, 1).Detrmine Duf(4,-1,6) for f(x,y,z) = e^x2y + 4zx3 in direction of (-3,2,6).
- The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are attached to the ends of a light inextensible string. The string is taut and passes over a small smooth pulley fixed at the intersection of a horizontal surface and an inclined plane.The block can move on the horizontal surface, which is rough. The particle can move on the inclined plane, which is smooth and which makes an angle of θ with the horizontal where tanθ = 3/4The system is released from rest. In the first 0.4 seconds of the motion P moves 0.3m downthe plane and B does not reach the pulley.(a) Find the tension in the string during the first 0.4 seconds of the motion.(b) Calculate the coefficient of friction between B and the horizontal surface.in b part, system gives an error that t is not defined for the frictionless spring question.Convert ∫50∫25−y2√0∫50−x2−y2√x2+y2√(x2+y2+z2)dzdxdy∫05∫025−y2∫x2+y250−x2−y2(x2+y2+z2)dzdxdy into spherical coordinates.
- A forceF = (5, 8)moves an object from the point (1, 3) to the point (10, 5). Find the work done by this force.Find the angle between the planes 3x – 2y + z + 4 = 0 and x + 4y – 3z – 3 = 0. Express your answers in DMS.Suppose L(5, 4) was reflected across the line y = x then translated along the vector <4, 0>. What is the y-coordinate of L''?
