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# 325 Review Sheet for MATH 231 at PSU

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 19 views.

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Date Created: 02/06/15

Math 231 Fall 2008 Review sheet for Exam 1 Our midterm exam will cover Chapters 13 14 Some important skills Section 131 Threedimensional Coordinate Systems 0 Find the distance from a point P to the coordinate planes or the coordinate axes 0 Find the distance between two points in R3 0 The general equation of a plane and general equation of a sphere in R3 0 Find the equation of a sphere 0 Find the radius and the center of a sphere given by a quadratic equation Sections 132 133 Vectors The dot product 0 Adding vectors triangle law parallelogram law scalar multiplication 0 Find the dot product of two vectors 0 Given a vector V in R3 nd its magnitude length or norm 0 Find a uriit vector that has the same direction as a given one 0 Apply the cosine formula 0 Determine whether two vectors are parallel perpendicular or neither 0 Scalar projection and vector projection of a vector b onto a 0 Find the work done by a force acting on an object Section 134 The crossproduct 0 Find the cross product of two given vectors 0 Find the area of the parallelogram 0 Find the area of of a triangle 0 Find a vector orthogonal to a given plane 0 Find the volume of a parallelepiped determined by vectors or points 0 Torque about a point Section 135 Equations of lines and planes 0 Find a vector parametric or symmetric equations of a given line L 0 Decide whether three given points lie in the same line 0 Find the equation of a given plane 0 Decide whether two lines lines are parallel intersecting or skew 1 0 Decide whether four given points lie in the same plane 0 Find the distance from a point P to a given plane 0 Find the distance between two parallel planes Section 136 Cylindrical and Quadratic Surfaces 0 Find traces of a surface S in the planes z k y k or z k 0 Find the traces of a given quadric surface and give a rough sketch 0 Identify cylinders in the space 0 Identify quadric surfaces ellipsoids paraboloids cones hyperboloids Section 141 Vector Functions and Space Curves 0 Describe a curve given by a vector function 0 Find limits and derivatives of vector functions 0 Find the parametric equations of a line segment from P to Q 0 Find the vector function that represents the curve of intersection of two given surfaces Section 142 Derivatives and Integrals of Vector Functions 0 Find the derivative of a given vector function 0 Find pararnetric or symmetric equation of the tangent line to a curve C at a given point 0 Find the unit tangent vector of a vector function r at a given point P Section 143 Arc Length and curvature 0 Find the length of a space curve 0 Pararnetrize a curve with respect to arc length 0 Find the curvature of a smooth space curve r ltftgt htgt 0 Find the normal vector N and binorrnal vector B at a given point of a space curve de ned by rt Section 144 Velocity and acceleration 0 Find the velocity speed and acceleration of a moving particle Pt 0 Find the normal and tangential components of acceleration 0 Given the acceleration initial velocity and position of a particle nd its velocity and its position vector at time t

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