How do you know if two vectors are coplanar?

If the scalar triple product of any three vectors is 0, then they are called coplanar. The vectors are coplanar if any three vectors are linearly dependent, and if among them not more than two vectors are linearly independent.

What is the condition for two vectors to be coplanar?

Conditions for Coplanar vectors. If there are three vectors in a 3d-space and their scalar triple product is zero, then these three vectors are coplanar. If there are three vectors in a 3d-space and they are linearly independent, then these three vectors are coplanar.

What if two vectors are collinear?

Two vectors are collinear if relations of their coordinates are equal, i.e. x1 / x2 = y1 / y2 = z1 / z2. Note: This condition is not valid if one of the components of the vector is zero. Two vectors are collinear if their cross product is equal to the NULL Vector.

What is the condition of coplanarity of two lines?

Two lines are said to be coplanar when they both lie on the same plane in a three-dimensional space.

Are two vectors orthogonal?

We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product of the two vectors is zero.

Are coplanar and collinear the same?

Collinear points lie on a single straight line. Coplanar points lie on a single plane.

What is electronic coplanarity?

In the electronics industry, the term “coplanarity” means the maximum distance that the physical contact points of a surface-mount device (SMD) can be from its seating plane. The number given for coplanarity defines the maximum gap that can exist from the underside of any pin to the PCB to which it is being soldered.

What is coplanarity equation?

The corresponding mathematical condition, known as the coplanarity equation, implies that the two camera stations, the two image points, and the object point are in a same epipolar plane. The coordinates of the object point do not appear in the equation, so no approximations for the coordinates are needed.

How do you determine if a vector is orthogonal?

Definition. Two vectors x , y in R n are orthogonal or perpendicular if x · y = 0. Notation: x ⊥ y means x · y = 0. Since 0 · x = 0 for any vector x , the zero vector is orthogonal to every vector in R n .