Vector Algebra

Gives the displacement vector from point A to point B in three-dimensional space.

Gives the length or Euclidean norm of a vector given in rectangular components.

Gives a vector of unit magnitude in the direction of a given non-zero vector.

Gives the position vector of a point dividing the segment joining points a and b in the ratio m:n internally (+) or externally (-).

Defines the scalar product of two vectors geometrically and in rectangular component form.

States the necessary and sufficient condition for two non-zero vectors to be perpendicular.

Gives the cosine of the angle theta between two non-zero vectors.

Gives the scalar projection of vector a onto vector b.

Evaluates the cross product of two vectors in rectangular component form using a 3x3 determinant.

States the collinearity or parallelism condition for two vectors in scalar multiple and cross product form.

Calculates the area of a triangle formed by two adjacent side vectors a and b.

Calculates the area of a parallelogram with adjacent sides represented by vectors a and b.

Computes the box product representing the signed volume of the parallelepiped formed by three vectors.

States the condition that three vectors are coplanar if and only if their scalar triple product is zero.

Expands the vector triple product into a coplanar combination of b and c using the BAC-CAB rule.