Calculus3Consider the vectors ~m = h3, −4, 1i and ~n = h−1, 7, 6i. (a) Find the vector and parametric equations of a line through the point (0, 2, −5) in thedirection of ~m.(b) Where does your line from part (a) intersect the plane 3x + 5y + z = −15?(c) Find the scalar equation for a plane containing both ~m and ~n*Please explain in as much detail as possible. (4) Consider the vectors i = (3, –4, 1) and ñ = (-1, 7, 6). If you are interested, you can go tohttp://bit.ly/fall2020calc3hw4 to view a 3D model created for this problem.(a) Find the vector and parametric equations of a line through the point (0, 2, –5) in thedirection of m.(b) Where does your line from part (a) intersect the plane 3x + 5y + z = -15?(c) Find the scalar equation for a plane containing both i and ñ.

Answered: Image /qna-images/answer/36b160fe-daf9-4967-b921-31a45cb80b1b.jpg

(4) Consider the vectors i = (3, –4, 1) and ñ = (-1, 7, 6). If you are interested, you can go to http://bit.ly/fall2020calc3hw4 to view a 3D model created for this problem. (a) Find the vector and parametric equations of a line through the point (0, 2, –5) in the direction of m.

(4) Consider the vectors i = (3, –4, 1) and ñ = (-1, 7, 6). If you are interested, you can go to http://bit.ly/fall2020calc3hw4 to view a 3D model created for this problem. (a) Find the vector and parametric equations of a line through the point (0, 2, –5) in the direction of m.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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Question

Calculus3

Consider the vectors ~m = h3, −4, 1i and ~n = h−1, 7, 6i.

(a) Find the vector and parametric equations of a line through the point (0, 2, −5) in the
direction of ~m.
(b) Where does your line from part (a) intersect the plane 3x + 5y + z = −15?
(c) Find the scalar equation for a plane containing both ~m and ~n

*Please explain in as much detail as possible.

(4) Consider the vectors i = (3, –4, 1) and ñ = (-1, 7, 6). If you are interested, you can go to
http://bit.ly/fall2020calc3hw4 to view a 3D model created for this problem.
(a) Find the vector and parametric equations of a line through the point (0, 2, –5) in the
direction of m.
(b) Where does your line from part (a) intersect the plane 3x + 5y + z = -15?
(c) Find the scalar equation for a plane containing both i and ñ.

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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