Let A be the point with coordinates (4, 4, 1), let B be the point with coordinates (0, 0, 3), let C be the midpoint of the line segment AB, let D be the point with coordinates (1,0,0), and let E be the point with coordinates (0,1,0). Let II be the plane passing through the three points C,D,E. Suppose that the line x=y=z intersects the plane II at the point P. Write down the first coordinate of P. [Please enter your answer numerically. You will be marked correct as long as what you enter is within 0.5 of the correct answer.]

Q: Let L, be the line passing through the point P=(8, -6, 0) with direction vector a=-3, 3, 1]", and…

A: Given, L1 is the line passing through the point P1=8,-6,0 with the direction vector d1→=-3,3,1T. So,…

Q: Let A be the point with coordinates (1, 9, 5), let B be the point with coordinates (-3, 5, 1), let C…

A: Given coordinates are, A=1,9,5B=-3,5,1 So, the midpoints of AB is C1-32,9+52,5+12=C-1,7,3.

Q: 9. Find the equation for the plane through Po(-2,3,9) perpendicular to the line x = -2 – t, y = -3 +…

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Q: Let A be the point with coordinates (3, -7, -2), let B be the point with coordinates (1, -9, -4),…

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Q: Consider the line that contains the point (2, -3, 5) and that has the direction vector (1, 2, 4). a)…

A: Given: The line passing through the point 2,-3,5 and having direction vector 1,2,4, To find: The…

Q: 5) Find the equation of the plane through the following point that also contains the given line. P =…

A: To find the equation of a plane through a point and parallel to a given line, we can use the…

Q: 3. Write an equation of the plane that is determined by the lines given by == and ==국 -2 z-2 -3 4 -1

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Q: iven the points A(2,6,0) and B(3,5,6) determine the point of intersection of this line to x-z plane.

A: Given points are A(2,6,0) and B(3,5,6) The line joining points (x1, y1, z1) and (x2, y2, z2) have…

Q: Let A be the point with coordinates (-6, -2, 0), let B be the point with coordinates (0, 4, -2), let…

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Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

Q: Let Lz be the line passing through the points Q1=(1, 3, 1) and Q2=(7, 12, 4). Find a value of k so…

A: We will solve the problem

Q: Let A be the point with coordinates (0, -2, -3), let B be the point with coordinates (2, 0, 3), let…

A: Equation of plane through three given points is given by…

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

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Q: 8. Given the points A = (1, 2, 4), B = (-1, 1, 3), and C = (-3, -2, 5). Find the equation of the…

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Q: Let A be the point with coordinates (4, 4, 3), let B be the point with coordinates (2, 2, 3), let C…

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Q: 2) Find the symmetric equation of the line containing the point (1, 2, 1) and perpendicular to the…

A: consider the direction ratio of line  contaning the point ( 1, 2 ,1 )  is  l , m, n