# ModelCourses/Calculus/Vectors/Vectors in Space

Vectors in Space

• Vector Algebra
• The right-handed coordinate system, three axes, three coordinate planes and eight octants
• Sketch a point in space.
• Sketch a line that passes through a given point and is parallel to an axis.
• Sketch a plane that contains a point and is parallel to a coordinate plane.
• Sketch a plane that contains a point and is perpendicular to an axis.
• Express a vector from Point A to Point B in vector notation.
• Sketch a position vector.
• Vector algebra: (1) scalar multiplication; (2) vector addition and subtraction
• Compute and sketching a scalar times a vector and a sum (difference) of two vectors.
• Triangle inequality
• Dot Product and Applications
• Two definitions of dot product of two vectors
• Angle between two vectors
• Compute the dot product of two vectors.
• Compute the angle between two vectors.
• Determine if two vectors are parallel or orthogonal (perpendicular) when the cosine of the angle between these two vector is 1, -1, or 0.
• Determine if the angle between two vectors is acute or obtuse when the dot product of these two vectors is positive or negative.
• Create a vector v that is parallel to a given vector.
• Create a vector v that is orthogonal to a given vector.
• Given a vector u and an angle theta, create a vector v such that the angle between u and v is theta.
• Projection and component of vector u onto vector v
• Compute the work done by a force vector along a direction vector.
• Compute the distance from a given point to a given line.
• Compute the distance between two planes.
• Cross Product and Applications
• Definition of the cross product of two vectors in space
• The cross product of vectors u and v is orthogonal (perpendicular) to u and v and satisfies the right-handed rule.
• Given two vectors u and v that are not parallel, find a vector which is orthogonal to both u and v.
• Compute the area of the parallelogram whose two sides are formed by two given vectors.
• Compute the volume of the parallelepiped whose three sides are formed by three given vectors.