Suppose we need to find an equation of the plane that passes through (1, 2, -2) that contains the line:X = 2t, y = 3-t, z = 1 + 3t. A normal vector to the required plane is: 2 (input a number from below) O<-6, - 9, 1) (2 (2, – 1, 3) (3 <1, 2, – 2)(4) The answer is not given. The equation of the required plane is ax + by + cz = d, where (a, b, c, d) = (input a number from below) (1 (6, 9, – 1, 26) (2 (2, – 1, 3, 0) (3 (-6, - 9, 1, -24) (4 The answer is not given.

Suppose we need to find an equation of the plane that passes through (1, 2, -2) that contains the line:X = 2t, y = 3-t, z = 1 + 3t. A normal vector to the required plane is: 2 (input a number from below) O<-6, - 9, 1) (2 (2, – 1, 3) (3 <1, 2, – 2)(4) The answer is not given. The equation of the required plane is ax + by + cz = d, where (a, b, c, d) = (input a number from below) (1 (6, 9, – 1, 26) (2 (2, – 1, 3, 0) (3 (-6, - 9, 1, -24) (4 The answer is not given.

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 2E

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Question

find normal vector/equation of a plane containing a point and parallel to a line containing that point

Suppose we need to find an equation of the plane that passes through (1, 2, -2) that contains the line:X = 2t, y = 3-t, z = 1 + 3t.
A normal vector to the required plane is: 2
(input a number from below)
(1 <-6, -9, 1> (2 (2, – 1, 3) (3 <1, 2, – 2>4) The answer is not given.
The equation of the required plane is ax + by + cz = d, where (a, b, c, d)
(input a number from below)
(1 (6, 9, – 1, 26) (2) (2, - 1, 3, 0) (3 (-6, - 9, 1, -24) (4 The answer is not given.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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