Question

1. Find the vector equation of a plane a) passing through the point A(-1,2,-3) and parallel to the vectors u = (-2,1,0) and v = (2,-3,-1) b) passing through the points A(2,3,2) and B(2,1,5) and C(3,-1,0) c) passing through the origin and containing the line r = (1,-3,2) + t(1,1,1) d) passing through the point A(2,-1,3) and is parallel to the yz-plane.

          1. Find the vector equation of a plane
a) passing through the point A(-1,2,-3) and parallel to the vectors u = (-2,1,0) and v = (2,-3,-1)
b) passing through the points A(2,3,2) and B(2,1,5) and C(3,-1,0)
c) passing through the origin and containing the line r = (1,-3,2) + t(1,1,1)
d) passing through the point A(2,-1,3) and is parallel to the yz-plane.

1. Find the vector equation of a plane
a) passing through the point A(-1,2,-3) and parallel to the vectors u = (-2,1,0) and v = (2,-3,-1)
b) passing through the points A(2,3,2) and B(2,1,5) and C(3,-1,0)
c) passing through the origin and containing the line r = (1,-3,2) + t(1,1,1)
d) passing through the point A(2,-1,3) and is parallel to the yz-plane.

Added by Anthony K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Manisha Sarker

Step 1

Since the plane is parallel to both u and v, the normal vector will be the cross product of u and v: n = u × v = (-2, 1, 0) × (2, -3, -1) = (1, 2, 5) Now, we can use the point-normal form of the plane equation: 1(x + 1) + 2(y - 2) + 5(z + 3) = 0 So, the vector Show more…

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1. Find the vector equation of a plane a) passing through the point A(-1,2,-3) and parallel to the vectors u = (-2,1,0) and v = (2,-3,-1) b) passing through the points A(2,3,2) and B(2,1,5) and C(3,-1,0) c) passing through the origin and containing the line r = (1,-3,2) + t(1,1,1) d) passing through the point A(2,-1,3) and is parallel to the yz-plane.