Question

Given the vectors 3x - 6y - 2z = 15 and 2x + y - 2z = 5, (a) Find a vector parallel to the line of intersection of the planes. (b) Find the equation of the plane given the points (3, -1, 0) using part (a). (c) Find the parametric equations using the given points from part (a) and (b). (d) Find the angle between the given planes.

Name: given the vectors 3x 6y 2z 15 and 2x y 2z 5 a find a vector parallel to the line of intersection of the planes b find the equation of the plane given the points 3 1 0 using part a c find the 10308
Uploaded: 2022-06-21T09:34:27-08:00
Duration: 5 min 54 s
Channel: Shyam P
Description: given the vectors 3x 6y 2z 15 and 2x y 2z 5 a find a vector parallel to the line of intersection of the planes b find the equation of the plane given the points 3 1 0 using part a c find the 10308

          Given the vectors 3x - 6y - 2z = 15 and 2x + y - 2z = 5, (a) Find a vector parallel to the line of intersection of the planes. (b) Find the equation of the plane given the points (3, -1, 0) using part (a). (c) Find the parametric equations using the given points from part (a) and (b). (d) Find the angle between the given planes.

Added by Mackenzie W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shyam P

06/21/2022

Step 1

The normal vectors are n1 = <3, -6, -2> and n2 = <2, 1, -2>. Calculating the cross product: n1 x n2 = <(-6)(-2) - (-2)(1), (-2)(2) - (3)(-2), (3)(1) - (-6)(2)> = <10, 8, 15>. Therefore, a vector parallel to the line of intersection of the planes is <10, 8, 15>. Show more…

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Given the vectors 3x - 6y - 2z = 15 and 2x + y - 2z = 5, (a) Find a vector parallel to the line of intersection of the planes. (b) Find the equation of the plane given the points (3, -1, 0) using part (a). (c) Find the parametric equations using the given points from part (a) and (b). (d) Find the angle between the given planes.