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Evaluate the following expressions.
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- Show that the point 1, - 2, 0 lies on both planes 3x-2y+z=7 and x-4y-2z=9. Hence, find the vector equation of intersection of both planesThe distance from the point Q = (2,0,3) to the plane π: 2x−y+2z = 2 corresponds to?Find the acute angle of intersection between the two planes 2x−4y + 4z = 6 and 6x + 2y−3z = 4
- 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.Find the point on the plane x−3 y+3 z =−8 that is closest to the point (−2,−2,0) . ( , , )The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid?