Which of the following scenarios are required to be able to determine a plane? Two non-collinear points Three noncollinear points Two parallel and non-coincident lines A line and a point not on the line one parallel line Two intersecting lines a line and a point on that line.

Q: Consider three points in three-dimensional space: ?=(11,2,−3),?=(2,−3,11),?=(−3,11,2) Let ? be the…

A: Let us consider the given points be To find the equation of plane containing the points A, B and C.…

Q: Which one is the point of intersection of the plane - 3x + 3y + 4z = 49 and the line x = 3-51 y =…

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Q: 4. Points P(1, 2, 0), Q(2, 3, -1) and R(-1, 1, 5) lie on a plane. Find the Cartesian equation of the…

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Q: a) Explain fully, atleast three possible relationships between two lines in R3 [c3] b) Which of the…

A: (a) The relationship between any two lines in ℝ3 is always one of the following three: They can be…

Q: b. A plane is uniquely determined by one point on the plane and two non-parallel vectors that are…

A: I have solved the question. Please go through that.

Q: Which of the following scenarios are required to be able to determine a plane? Two parallel and…

A: A plane is a two-dimensional flat surface that extends infinitely in all directions. It is defined…

Q: Find the point of intersection of the line with equation (1,8,3) + t(1,-1,3) and this plane. What is…

A: Now we will find the point of intersection.  And we  will find the y coordinate of this point

Q: ) Find the equation of the plane containing the following 3 points. (-1,2, –3), (4,0,9), (-3, 1,7)

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Q: Question 3. Do the lines x=t, and x = 2t - 2, y = 2t - 1, 2 = 3t+1 intersect each other at only one…

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