• #### The Resultant of Two Forces - Concept

##### Math›Precalculus›Vectors and Parametric Equations
How to find the resultant of two forces when they are parallel, opposite, or perpendicular in direction.
• #### Navigation Problems - Concept

##### Math›Precalculus›Vectors and Parametric Equations
How we measure airspeed, wind, groundspeed, and other variables in navigation.
• #### Introduction to the 3D Coordinate System - Problem 1

##### Math›Precalculus›Vectors and Parametric Equations
How to find the coordinates of the vertices of a rectangular box.
• #### The Midpoint and Distance Formulas in 3D - Problem 1

##### Math›Precalculus›Vectors and Parametric Equations
How to find the length and midpoint of a segment in three dimensions.
• #### Vector Quantities - Scalar Quantities

##### Science›Physics›Linear and Projectile Motion
Understanding the differences between vectors and scalar quantities.
• #### The Midpoint and Distance Formulas in 3D - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to find the equation of a sphere with center (a,b,c) and radius r.
• #### Adding Vectors - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to plot the sum of two vectors (one the opposite of the other) and find its magnitude.
• #### Area With the Cross Product - Problem 1

##### Math›Precalculus›Systems of Linear Equations and Matrices
How to compute the area of a parallelogram using the cross product of the vectors that determine it.
• #### The Resultant of Two Forces - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to find the resultant of two forces at an acute angle (45 degrees).
• #### Unit Vectors - Problem 3

##### Math›Precalculus›Vectors and Parametric Equations
How to find a unit vector in any direction given the direction's angle.
• #### The Angle Between Planes - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to find the angle between two planes.
• #### Vector Operations in 3D - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to find the angle between two vectors in three dimensions.
• #### Motion Along a Line - Problem 1

##### Math›Precalculus›Vectors and Parametric Equations
How to write equations describing motion in a straight line given the velocity and the position when t=2.
• #### Area With the Cross Product - Problem 3

##### Math›Precalculus›Systems of Linear Equations and Matrices
How to compute the area of a triangle in xyz-space using vectors formed from two of its sides.
• #### The Dot Product of Vectors - Problem 3

##### Math›Precalculus›Vectors and Parametric Equations
How to prove that the dot product uu of a vector with itself equals the square of its magnitude abs(u)^2.
• #### Introduction to the 3D Coordinate System - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to find the equation of a sphere with radius r when it is centered at the origin.
• #### Algebraic Representation of Vectors - Problem 1

##### Math›Precalculus›Vectors and Parametric Equations
How to express a vector from point Q to point R algebraically in component form <a,b>.
• #### Motion Along a Line - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to find the velocity and speed, and the displacement and distance traveled, of an object traveling in a straight line.
• #### Navigation Problems - Problem 3

##### Math›Precalculus›Vectors and Parametric Equations
How we find the course and groundspeed of an airplane when we are given its velocity and the wind velocity.
• #### Navigation Problems - Problem 1

##### Math›Precalculus›Vectors and Parametric Equations
How we find the course and groundspeed of an airplane when we are given its velocity and the wind velocity.