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- the xyz-plane determine the distance and angle from point (2,1,1) in the space and two planes (x-y-2z=9) and ( x+y+z=4).Find the coordinates of the point (x, y, z) on the plane z = 3 x + 3 y + 3 which is closest to the origin. x=-----y=------z=-----Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1 in the affine space and then in the projective space by using homogeneous coordinates. Complex solutions are valid. Please show your steps for both affine space and in project space. Box your final answer.
- 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.Vectors are drawn from the center of a regular n-sided polygon in the plane to the vertices of the polygon. Show that the sum of the vectors is zero. (Hint: What happens to the sum if you rotate the polygon about its center?)The acute angle of intersection of yz plane and the plane 2x-y+z-4=0 is:
- Vectors are drawn from the center of a regular n-sided polygon in the plane to the vertices of the polygon. Show that the sum of the vectors is zero. (Hint: What happens to the sum if you rotate the polygon about its center?) Let P be a regular n-sided polygon in a plane, where the center of the polygon is the center of the plane and where the x-axis goes through at least one of the vertices. If the sum of the vectors for an n-sided polygon is zero, will the sum always be zero, no matter how the polygon is rotated? YES or NO? Explain your answer.Point W is the centroid of triangle TRV. VX = 204 and RW = 104. The length of RY = ____.Triangle XYZ in 3d has vertices X=(0,1,2), Y=(3,-2,1), and Z=(2,-1,0) normal vector to the plane that has XYZ has the form A→=(x,4,-6) find x