1. Let P(1, 1,-1), Q(1,2,0), and R(-1,0,0) be given points. Give the equation of the plane containing the point R, that is orthogonal to the plane 2x - y + 5z -3= 0 and that is parallel with the vector PQ.

Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

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Q: Let P and Q be the points in R3 with position vectors p = (4, -6, 1) and q = (1, -3, -5),…

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Q: III. Consider the line ₁ given by the symmetric equations +1=-y-1 B 2 and the line ₂ given by the…

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Q: Find the vector equation of the plane that contains the parallel lines [x, y, z]= [0,1,3] + [-6,…

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Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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Q: Determine the point at which the line passing through the points P(1, 0, 6) and Q(7, -1, 7)…

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Q: Find an equation of the plane that passes through the point (1,2,3) and which is orthogonal to the…

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Q: Given the points A(3,-1,1), B(2,3,4) and C(4,1,1). (a) Find a unit vector that is simultanously…

A: Concept: A plane going through three non-collinear points has the following equation: Vectors and…