Let L₁ be the line parametrized by (4-2t, 2-t, 3+t). Let L₂ be the line parallel to L₁ going through the point (0, -2, 1). A. Give a parametrization for L₂. B. Find an equation for the plane which contains both lines.

Q: Find parametric equations for the line in which the planes, x+2y-2z=5 and 5x-2y-z=0 intersects. Show…

A: Given, The equation of intersecting planes, x+2y-2z=5 and 5x-2y-z=0.   We have, x + 2y = 2z + 5 and…

Q: Write the vector equation for the line of intersection between the planes π1:x−z=−5 and π2:x−y=−1.

A:

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A:

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A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

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A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Describe the plane x = 4.

A: Given, plane x=4we have to describe the plane x=4

Q: Find parametric equations for the line in which the planes, X+2y-2z=5 and 5x-2y-z=0 intersects. Show…

A:

Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: Line A goes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A and passes…

A: Given: Line A passes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A. Line…