3. A scalar equation of the plane with normal vector = [0, -1, 3] and passing through the - point (5,-2, 3) is: B) y-32-11-0 A) y-3z +11-0 E) None of the above C) -y+ 3z + 11-0 D) -y+ 3z + 16-0

Q: How would I find the equation of the line through points (1,2,0) and (1,4,1) in parametric vector…

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Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

A: Solution :

Q: If a line is parallel to the vector 2i + 9j + 8k and passes through the point P = (6, 8, 8), then…

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Q: Let a = (6, −3, −5) and b = (7, -2, 10) be vectors. (A) Find the scalar projection of b onto a.…

A: Let  be vectors.(A) To find the scalar projection of .(B) To decompose the vector  into a component…

Q: Find a scalar equation of the plane containing the line and the point (-5, -1,5). x = 6 +8t, y=-1-3t…

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Q: Find the angle between the planes whose vector equations are 7-(2i + 2)- 36) =57-(3i -3) + Sk) = 3…

A: The solution to the the given question is explained below.

Q: Plane passing through point P0 (1, 2, 1) and perpendicular to vector (1, -1, 2) Find the equation…

A: Given:  Plane D1 : passing point P0(1, 2, 1)                 perpendicular vector (1, -1, 2) Plane…

Q: Q1) Find the equation of the plane passing through the point (4,-1,-5) and perpendicular to the…

A: We have to find the equation of the plane passing through the point (4,-1,-5) and perpendicular to…

Q: Let A= (-1,3,3) B= (4,-1,0) C= (5,4,-7) D= (2,-1,-1) i) the normal vector to the plane ABC. ii) the…

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Q: 2. Find the equation of the planes: a) (in general form) that goes through the three points A(4, 0,…

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Q: 3. Does the parametric equation r = (2,-5,2) + s(1,4,2)+(-2,-3,1), s,/€ R, and the vector equation…

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

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Q: Find the intersection of the line that passes through (0,3,-1), in the direction of…

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Q: Find the vector equation for the line of intersection of the planes x + y - 4z = 4 and + 4z = -2

A: We have to find the vector equation.

Q: - a) Determine the vector equation of the line of intersection of these 2 (1) x + 2y + 2z = -3 (2 2x…

A: Note:  part(b) is the independent subpart of part(a) and also it is incomplete. so part (b) can't be…

Q: A plane contains the point B(-3, 2, -4) and the line with parametric equations x= 1 + 2?, y = −t, z=…

A: Explanation of the answer is as follows

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: Find parametric equations for the line through p (2,3,0) and perpen-dicular to the vectors u =(1,…

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