Triangle Law of Vectors

If two vectors acting at a point are represented in magnitude and direction by the two sides of a triangle taken in one order, then their resultant is represented by the third side of the triangle taken in the opposite order.

If two vectors A and B acting at a point are inclined at an angle θ, then their resultant

R = √A² + B²+ 2AB cos θ

If the resultant vector R subtends an angle β with vector A, then tan β = B sin θ / A + B cos θ

2. Parallelogram Law of Vectors

If two vectors acting at a point are represented in magnitude and direction by the two adjacent sides of a parallelogram draw from a point, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram draw from the same point.

Resultant of vectors A and B is given by

√A2+ B²+ 2AB cos θ

If the resultant vector R subtends an angle β with vector A, then tan β = B sin θ / A + B cos θ