Multivariable Calculus (Calc III) - Complete Semester Course - How to find lines and planes, Multivariable Calculus

(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