Vector Operations

Consider two force vectors in a two-dimensional coordinate system.

These vectors can be added using the parallelogram law, where the tails of the concurrent vectors are joined together and lines parallel to each vector are drawn to form a parallelogram.

The resultant vector can be obtained by drawing a diagonal from the tails to the point of intersection of lines.

Similarly, the vectors can be added using the triangle rule, where two vectors are arranged as two sides of the triangle joined head-to-tail, and the third side of the triangle represents the magnitude and direction of the resultant vector.

Vector subtraction is similar to adding reverse of one vector to another. As a result, the difference between two vectors is obtained using the same rules of vector addition.

When a vector is multiplied by a scalar, the magnitude of the vector varies by the amount of the scalar quantity.

If the scalar is positive, then the direction of the vector remains the same, and if it is negative, the direction is reversed.