Given points A(1,2,3), B(0,-3,-2) and C(-1,0,5): a) Determine vector, parametric and symmetric equations of the line that goes through points A and B. Then, find the coordinates of 2 additional points on this line. b) Determine vector and scalar equations of the plane that contains points A, B and C. Then, find the coordinates of 2 additional points on this plane.

Q: Given the point A(2,1,-3) and B(6,-1,-5) write the vector equation and the parametric equations of…

A: Once we get vector form of the equation we can easily write the parametric form of equation of line.

Q: Based on the points A(5,6,7), B(6,7,12), C(7,12,5). Write the equation of your plane in Vector,…

A: Step 1:​Three points are…

Q: 2. Given a line that passes through the point (-2,1,3) and is parallel to the line joining A(1,5,3)…

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Q: Find the requested vector in R2 where A = (-3, 6), B = (8, –6) and C = (7,4). -2AB + 7CB = help…

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Q: Find the vector and parametric equations of the line through the points A = (2,4,7) and B =…

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Q: Problem 1 Instructions: Given mZSTU = 48°, find m ST. 48° U mST Check

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Q: Find an equation of the plane through the three points P = (0, 0, 4), Q = (-3, 4, 0), R = (-1, -2,…

A: The given problem is to find the equation of plane passing through the given 3 points P(0,0,4),…

Q: 1. Draw the vector V that goes from the origin to the point (-4, -6). (a) Find V (b) Write V in…

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Q: perpendicular to (x, y, z) = (1, -2,0) + r(1, -1, 1) through P(1, 3,5) [parametric equations]

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Q: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

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Q: Write the parametric equations of the line through the point (1,2,3) parallel to the vector a =.…

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Q: Use the cross product to find an equation for the plane that passes thru the points (1, 2, 3), (4,…

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Q: Line E goes through the points (1, 5, 2) and has the direction vector ⟨2, 2, 3⟩. Line F goes through…

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Q: Consider the line passing through the points (2, -3,4) and (5,10, -12). Describe the line by a.…

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Q: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

A: Here we have to find the equations for the lines,  a) The line through the point P(3,-4,-1) and…

Q: Find an equation of the plane through the three points given: P= (0,0, 1) , Q =(-1,4,2), R=(-2,–2,…

A: We have to find the equation of a plane which passes through the following points -  P = (0,0,1) Q =…

Q: Determine a vector that is perpendicular to (2,-5,-1) and (4,0,1).

A: The problem is asking us to find a vector that is perpendicular to two given vectors. In vector…

Q: Q1: al Find parametric and vector equations for the line y-axis, then find the distant between the…

A: Since you have uploaded multiple question, according to our guidelines we have solved first question…