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Please provide all steps and state the answer, please and thank you.
1.
Determine parametric equations for the plane through the points A(2, 1, 1), B(0, 1, 3), and C(1, 3, −2).
2.
Determine a vector equation for the plane that is parallel to the xy -plane and passes through the point (4, 1, 3).
Please provide all steps and state the answer, please and thank you.
1. Solve the following system of equations and give a geometrical interpretation of the result.
x + y + z = 6
2x + y − 3z = -5
4x − 5y + z = −3
2. Give a geometrical interpretation of the intersection of the planes with equations
x + y − 3 = 0
y + z + 5 = 0
x + z + 2 = 0
1.
a) Determine the symmetric equations for the line through P(5, 6, 10) and parallel to the line with equation Vector r = (6, 1, 1) + t(−2, 1, 3).
b) Determine two other points on this line
2.
Explain why there are many different vector and parametric equations for a line.
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