Question

Use lagrange multipliers to find the distance from the point (2, 0, 1) to the plane 7x 5y + 9z + 1 = 0.

Answer 1

1) Use Lagrange multipliers to find the distance from the point (2, 0, −1) to the plane 7x − 5y + 9z + 1 = 0.

2)Let c1(t) = eti + (sin(t))j + t3k and c2(t) = e−ti + (cos(t))j − 2t3k. Find the stated derivatives in two different ways to verify the differentiation rules.

d/dt: {c1(t) · [2c2(t) + c1(t)]}