Calc 1,2,3

Question 1

Find angle between 2 lines

Answer 1

Cos(θ) = |u_d • u_D|

Question 2

Finding equation of the plane from points

Answer 2

1. ) Get two vectors from the point
2. ) Find cross product of the two vectors
3. ) Plug into equation of plane

a(x−x₀)+b(y−y₀)+c(z−z₀)=0

Use the common points of the two vectors

Question 3

Finding Directional Derivative

Answer 3

a. ) Find the unit vector ( vector divided by magnitude)
b. ) Find the gradient of the function ( partial derivative)
c. ) f(x,y,z) = f_x (x,y,z) a + f_y (x,y,z) b + f_z (x,y,z) c

where a, b, c => unit components

Question 4

Area of triangle with vectors

Answer 4

a. ) Get two vectors adajacent using the points
b. ) Find the cross product of the two vectors
c. ) Get the magnitude of the two vectors
d. ) Divide by 2