Example 4: Find the equation of the planethrough the point (-4, 3, 1) that is perpendicular tothe vector a = -4 i +7 j-2 k.Solution:

Find the equation of the plane through the point (-4, 3, 1) that is perpendicular to the vector a =…

Answered: Example 4: Find the equation of the…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.6: Equations Of Lines And Planes

Problem 1E

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Determine the vector, parametric, and Cartesian (Scalar) equations for the line that passes through A(4, –1) and is perpendicular to the line through points M( –4, 3) and N(2,0). Can you please solve this with a full explanation, thank you!
(a) Does the point P(2, −1, −3) lie on the plane given byΠ : 2x − y − 3z − 4 = 0? Justify your answer.(b) If the answer to (a) is yes, then find the vector equation of the line passingthrough P and perpendicular to Π.(c) If the answer to (a) is no, then find the vector equation of the line passingthrough P and perpendicular to Π
In Problem,the vector v has initial point P and terminal point Q.Write v in the form that is,find its position vector. P =(0, 0); Q =(-3, -5)
Find the vector, parametric, and symmetric equations of the line which passesthrough the points A = (3, 1, −1) and B = (7, 0, 1).
2.2 (4) Please try to answer & explain me this question. Determines the Cartesian equation of the plan passing through D (0, 5, -2) and containing the vectors m1 = [3, -1, 0] and m2 [2, 4, -1]
Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line. Point Perpendicular to (5, 2, 2) x-1/4 = y + 2 = z+5/-5
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Example 4: Find the equation of the plane through the point (-4, 3, 1) that is perpendicular to the vector a = -4 i+7j-2 k. Solution: