The resultant is the vector sum of two or more vectors. It is the result of adding two or more vectors together. If two or more velocity vectors are added, then the result is a resultant velocity. If two or more force vectors are added, then the result is a resultant force.

If two vectors are perpendicular to each other, then their dot product is equal to zero.

Vector diagrams are diagrams that depict the direction and relative magnitude of a vector quantity by a vector arrow. Vector diagrams can be used to describe the velocity of a moving object during its motion. In a vector diagram, the magnitude of a vector quantity is represented by the size of the vector arrow.

The space diagram takes care of the point of application of forces and the geometry of the truss. The above shown figure is only to get the reactions. Applied force is ab and force is bc in the vector diagram. Reaction is equal to da and Reaction is equal to cd in the vector diagram.

Starting from where the head of the first vector ends, draw the second vector to scale in the indicated direction. Label the magnitude and direction of this vector on the diagram. Draw the resultant from the tail of the first vector to the head of the last vector. Label this vector as Resultant or simply R.

Let’s work through it.

1. Step 1) Draw the vector.
2. Step 2) Add in the triangle legs.
3. Step 3) Math. y-direction = magnitude * sin(angle) = 5 meters * sin (37) = 3 meters. x-direction = magnitude * cos(angle) = 5 meters * cos (37) = 4 meters.
4. Step 4) Plug the solutions into the definition of a vector. Vector = 3 +4ŷ

The position function →r(t) r → ( t ) gives the position as a function of time of a particle moving in two or three dimensions. Graphically, it is a vector from the origin of a chosen coordinate system to the point where the particle is located at a specific time.

The formula for the magnitude of a vector can be generalized to arbitrary dimensions. For example, if a=(a1,a2,a3,a4) is a four-dimensional vector, the formula for its magnitude is ∥a∥=√a21+a22+a23+a24.

Angular displacement is a vector quantity, which means that angular displacement has a size and a direction associated with it. As the object rotates from point “0” to point “1”, it rotates about an axis, so the direction of the angular displacement is measured along the axis.