Cartesian coordinates
Vector Calculus for Engineers
Vector Operations using Cartesian Coordinates
A vector can be drawn with the base at the origin using unit
vectors i, j and k that have a length of 1 and point in the direction
of the three axes. To add vectors using Cartesian coordinates, we
can add the components of each vector. For example, the vector a
can be represented as a1i + a2j + a3k. The length of the vector
can be found using the Pythagorean theorem in three-dimensional
space. The position vector locates a point in space, while the
displacement vector is the difference between two position
vectors and is useful in many physical problems.
The length of a vector is represented by the absolute value sign. The components of a vector
can be multiplied by a scalar, and two vectors can be added by adding their components. The
displacement vector is the vector pointing from the head of one position vector to the other.
Cartesian coordinates originate from quaternions, which is a word for quaternionic that means
"nonsense." The length of a vector is used to define a factor of dimension such as space, time,
height, width, distance, weight, gravity, or origin.
Conclusion
Vector Calculus for Engineers
Vector Operations using Cartesian Coordinates
A vector can be drawn with the base at the origin using unit
vectors i, j and k that have a length of 1 and point in the direction
of the three axes. To add vectors using Cartesian coordinates, we
can add the components of each vector. For example, the vector a
can be represented as a1i + a2j + a3k. The length of the vector
can be found using the Pythagorean theorem in three-dimensional
space. The position vector locates a point in space, while the
displacement vector is the difference between two position
vectors and is useful in many physical problems.
The length of a vector is represented by the absolute value sign. The components of a vector
can be multiplied by a scalar, and two vectors can be added by adding their components. The
displacement vector is the vector pointing from the head of one position vector to the other.
Cartesian coordinates originate from quaternions, which is a word for quaternionic that means
"nonsense." The length of a vector is used to define a factor of dimension such as space, time,
height, width, distance, weight, gravity, or origin.
Conclusion
