Rotation of a Vector Definition, Formulas – Scalars and Vectors

Rotation of a Vector Definition, Formulas – Scalars and Vectors

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

Rotation of a Vector By an Angle:
(i) If a vector is rotated through an angle θ, which is not an integral multiple of 2π, the vector changes.
(ii) If the frame of reference is rotated or translated, the given vector does not change. The components of the vector may, however, change.

Resolution of Vectors into Two Components
If two-component vectors of R are OP and PQ in the direction of A and B, respectively, and suppose OP = λA and PQ = µB, where λ and µ are two real numbers.
Rotation of a Vector
Then, resultant vector, R = λA + µB

Resolution of a Vector into its Rectangular Components
Rotation of a Vector
If any vector A subtends an angle θ with X-axis, then its
horizontal component, Ax = A cos θ
Vertical component, Ay = A sin θ
Magnitude of vector, A = \(\sqrt{A_{x}^{2}+A_{y}^{2}}\)
tan θ = \(\frac{A_{y}}{A_{x}}\)
Angle, θ = tan-1\(\left(\frac{A_{y}}{A_{x}}\right)\)

Scalars and Vectors Topics:

Scalars and Vectors Tensors
Types of Vectors Addition of Vectors
Rotation of Vectors Direction Cosines of a Vector
Subtraction of Vectors Multiplication of Vectors
Scalar Product of Two Vectors Vector Product of Two Vectors
Division of Vectors