Copy of Following section 9.5.2, let's calculate the equation of a plane passing through: P1 = (1, 2, 3) P2 = (-4, 5, -6) P3 = (0, 3, 1) According to the book, what is a normal vector to the plane (not necessarily the "unit" vector n-hat)? (Follow their notation) (1,2,3) (-5,3,-9) (4, -2,7) (3,-1,-2)

Q: Develop vector and parametric equations for the line through (7,2,-1) and parallel to r = (4,7,0) +…

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Q: Give the parametric and symmetric equations of the line that passes through the point (4, -3,5) and…

A: Using the dot product equal to zero for perpendicular to the vectors.

Q: Give the vector equation of the line passing through P and Q. P = (5,2), Q = (3, 0) X = + t 00

A: To find the vector equation of the line passing through P and Q.P=5, 2, Q=3, 0

Q: 5. Determine a vector equation of the line that passes through the origin and is parallel to the…

A: Determine a vector equation of the line that passes through the origin and is parallel to the line…

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

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Q: Which of the following vectors is/not perpendicular to the line whose direction vector is (2,-3,5)?…

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Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

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Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

Q: P= (2,-2), Q = (4,0) ∙8-8 t X =

A: Vector equation of a line passing through two points with position vectors P(2,-2) and Q(4,0)…

Q: Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

A: We have to find a direction vector for the line containing the points -1, 5, 2 and 2, 3, -1. We know…

Q: P(2,5, 4) and Q(8,3,3) Let be the line through P in vector direction (1,2,3) and let II be the plane…

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Q: Give the vector equation of the line passing through P and Q. P= (3, 1), Q = (2, 0) X = + t

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Q: Which of the following can be the vector equation of the line passing through the points (3,2,1) and…

A: We have to find the vector equation of the line passing through the points (3,2,1) and (5/2,1,-2).

Q: nd the vector equation of a line that passes through the point (-2,1,0) and is parallel to the plane…

A: Follow the steps.

Q: Determine an equation (in variables x, y, z) for the plane through the point (8, 1, 4), and with…

A: GIVEN- EQUATION OF PLANE PASSING THROUGH THE POINT (8,1,4) AND WITH VECTOR (-2,6,-2) TO FIND-…