University:
Georgia Southern University
Course:
MATH 2243 | Calculus 3
Academic year:

2024
Views:

344

Pages:

1
Author:

Jalen W.

Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Student: Jalen Wilson Date: 07/11/24 Assignment: Section 12.5 Enhanced Assign 1. A line passes through the point (8,5,10), and is parallel to the vector 6i + 3j + 8k. Find the standard parametric equations for the line, written using the components of the given vector and the coordinates of the given point. Let z = 10 + 8t. x= 8 + 6t , y = 5 + 3t , z = (Type expressions using t as thevariable.) 10 + 8t 2. A line passes through the points P( − 9, − 8, − 2) and Q(9, − 10,3). Find the standard parametric equations for theline, written using the base point P( − 9, − 8, − 2) and the components of the vector PQ. Let z = − 2 + 5t. x= − 9 + 18t , y = − 8 − 2t , z = − 2 + 5t (Type expressions using t as thevariable.) 3. Find parametric equations for the line through the origin parallel to the vector 7j + 5k. Let z = 5t. x= 0 , y = 7t , z = (Type expressions using t as thevariable.) , − ∞ < t < ∞ 5t 4. Find parametric equations for the line shown below. Thex-axis Let x = t. The parametric equations are x = t (Type expressions using t as thevariable.) , y = 0 , z = 5. Graph the sets of points whose polar coordinates satisfy the inequalities π 4 0 ≤θ≤ 3π 4 . , 0 ≤ r ≤ 2. Choose the correct graph below. A. B. C. y y 1.6 y 1.6 1.6 -1.6 y 1.6 x -1.6 D. 1.6 x -1.6 -1.6 1.6 x -1.6 1.6 -1.6 x -1.6 1.6 -1.6 6. Find the equation for the plane through the point P0 = (5,6,3) and normal to the vector n = 3i + 5j + 8k. Using a coefficient of 3 forx, the equation for the plane through the point P0 = (5,6,3) and normal to n = 3i + 5j + 8k is 3x + 5y + 8z = 69 . (Type anequation.) 7. Find the equation for the plane through the points P0 ( − 1,5,5), Q0 ( − 4, − 2,2), and R0 (4,1,1). Using a coefficient of 16 forx, the equation of the plane is 16x − 27y + 47z = 84 . (Type anequation.)