Suppose the movement in the polar coordinate system is [0₁, d. 0₂]= [, 2, a. What will be the position of the robot if the original position is at [1,1,0]

Q: . Determine the corresponding Cartesian equation. [ L1: = [4,-3, 5] + t[2, 0,3], t € R and L2: 7 =…

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Q: 60. Show that the distance between two points P1(x1, y1) and P2(x2, y2) is invariant under rotation.…

A: For the points P1 and P2 , the distance between the points is given d(P1,P2)=(x2-x1)2+y2-y12 . For a…

Q: b. Find the projection of v with equation 2x -y + 4z = 0. 1 -3 on the plane

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Q: 11. Find parametric equations for the line that contains the points P(2, -4, 7) and Q(0, –3, 5).

A: If Px0 ,y0,z0 and Qx1,y1,z1 are any two points then the parametric equation of the line containing…

Q: If a line is parallel to the vector 8i + 5j + 3k and passes through the point P = (6,2,4), then the…

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Q: If a point, P1=[10,10,10], will be rotated by 60 degree about the Z-axis, find the final position…

A: Solution ) suppose P1 [ x1 y1 , z1] is rotated about z axis so new point P2 [ x2 , y2 , z2 ] is…

Q: Let P(3,-1,4) and Q(10, 13,9) u = (2,5, -1) and v= (7,-1,2) l be the line through P along direction…

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Q: Give two possible pairs of polar coordinates (r, 0) for the rectangular (Cartesian) point (-6, –6V3)

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Q: 4. Given that the Cartesian equations of line L is y = 3, x + 2 =z. A(2,1,0) and B(1,4,5) are two…

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Q: Consider three points in three-dimensional space: A = (5, 2, –7), B = (2, –7,5), C = (-7,5, 2). Find…

A: The parametric equation of a line passing through the point and in the direction of is defined by…

Q: Find the parametric equation. For.:. a the line passes through (1,2₁ +), (-1₁0, +/...

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: 15. Find the Cartesian equation of the following lines: a. parallel to the line r= 2i+3j+4k +1(3i –…

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Q: Find the parametric equations of the line perpendicular to l1 and l2 that contains the point (-1.…

A: We have to find equation of a line which is passes through the point (-1,-1,-1) and Perpendicular to…

Q: 1) The area of the triangle whose vertices are the points P(1,0,2), Q(3,-1,3), and R(4,1,2). 2)…

A: To find the following equations of line , and area of a triangle.  Since you have posted a question…

Q: 3. Show the parametric form of the line that passes through points A(3, 6, 1) and B(2,10, 5) Compute…

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answer as…

A: THE GIVEN LINE IS, x=y=z WE CAN REWRITE IT AS, x-01=y-01=z-01 SO, THE DIRECTION RATIOS FOR THE LINE…

Q: Give the vector equation of the plane passing through P, Q, and R. P = (8, 8, 8), Q = (4, 0, 2), R =…

A: The answer is given below:

Q: 10. Consider the Cartesian point (-2,-2). Determine the polar coordinates of this point.

A: Use cartesian to polar coordinate

Q: Express the 2D Cartesian  point P(5,10) in Polar coordinates

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Q: Compute the product of C(90°)B(180°)A(−90°) using the points A(6,2), B(1, 2) and C(6,-3). What are…

A: Given: The product of rotations, C90°B180°A-90° and the points A6,2, B1,2 and C6,-3.   To determine:…

Q: Sketch a possible graph of the function f given the graph of f' below. Assume that 3. f is…

A: A discontinuous graph of f' is given Both pieces of the function of the form of parabola. Assume…