16. Find the vector and Cartesian equation of the planes containing, a. the point 4(1,5, 3) and perpendicular to the vector d = 31-4/+6k. b. the points A(1,3, 4), B(2,-1,4) and C(-2,4,5).

Q: 32. Determine the vector equation of the plane that contains the following two lines. L1: = [4,-3,…

A: .

Q: Using the same vectors v = (1,3, 2) and w = (3,5,6) and the same poin P= (8,4,-2). Find the equation…

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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: A plane in R'is perpendicular to the vector (4, 2, – 9), and contains the point (- 9, 5, - 8). Find…

A: A plane in ℝ3 is perpendicular to the vector 4, 2, -9 and contains point -9, 5, -8To find the…

Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

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Q: If a line is parallel to the vector 4i + 10j + 7k and passes through the point P = (7,7,4), then the…

A: Solution

Q: b) Find parametric and vector equations for the line through (2,3,0) perpendicular to the vectors u…

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Q: Determine a unit vector perpendicular to the plane a =21-6j –3k and b=4i+3j – *

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 3) Find equations for the lines: The line through the point D/2 g. The line through (0,-7,0)…

A: Equation of line in 3D

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: - 3)² = 81 then, find its ce or a=<3, -1

A: 1. Given: The points are 2,3,-6 and -1, 4, 5 To find the distance between the given points. The…

Q: 3. A plane contains A(1, -3, 2), B(-2, 4, 2) and C(3, 2, 1). (a) Determine the vector equation of…

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Q: If a line is parallel to the vector 6i + 7j+ 2k and passes through the point P= (5, 1,7), then the…

A: Given that a line is parallel to the vector 6i+7j+2k and passes through the point P=5, 1, 7. We know…

Q: If a line is parallel to the vector 3i + 9j+ 6k and passes through the point P = (5, 5, 4), then the…

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Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: For parts (a)-(e), please use the following vectors: C = (-1,-1,0) -120°, and 0₂ = 90° A = (2,4,0) B…

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Q: If a line is parallel to the vector 7i +9j + 9k and passes through the point P = (10,4, 1), then the…

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