How to find lines and planes, Multivariable Calculus
Автор: Dr. Bevin Maultsby
Загружено: 2020-07-27
Просмотров: 5052
Описание:
(Unit 1 Lecture 16) Examples in this lecture:
1. Find a vector equation for the plane that contains the point P (1, −3, 0) and the line with parametric
equations x = 3 − 8t, y = −3 + 5t, z = 2 + 2t. Error in Example 1: when I cross the vectors, I dropped a negative sign--but the process is correct. If you fix it (so that it's (-2,0,-2) not (-2,0,2)), the plane is x+2y-z = -5.
2. Find the point of intersection for the lines r = ⟨2,0,1⟩ + t⟨−1,1,1⟩ and r = ⟨4,−5,8⟩ + t⟨2,−3,1⟩. Then find the plane containing these two lines.
3. Find the distance from the point P(2,1,3) to the line r = ⟨1,0,1⟩ + t⟨−1,3,2⟩.
4. Find the angle of intersection between the planes 3x−y+6z=10 and x+2y−5z=0. Then find the line of intersection.
#mathematics #math #multivariablecalculus #calculus #vectorcalculus #iitjammathematics #calculus3
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