Lami’s theorem in vector:
Lami’s theorem is used to relate forces with angle between them when three coplanar forces are acting from a point in equilibrium. The ratio of one force to the sine of angle between other two forces is constant. Statement and prove: According to Lami’s theorem that for a triangle, the ratio of one side with […]
Explore MoreDefinition and representation of vector (Class – 11)
Scalar: The quantities which are represented by magnitude and have no directions and follow the ordinary algebra are called scalar quantity. Example: mass, volume, speed, density etc. Vector: The quantities which are represented by magnitude and directions and follow a special type of algebra (vector algebra) are called vector quantity. Example: velocity, acceleration, force etc. […]
Explore MoreVector cross product
Vector product or cross product: The vector product of two vectors and is defined as the product of the magnitudes of and and the sine of the angle between them. If and creates angle θ then = AB. Where is the unit vector perpendicular to the plane of and . Properties of cross product: (i) […]
Explore MoreVector dot product
Scalar product or dot product: The scalar product of two vectors and is defined as the product of the magnitudes of and and the cosine of the angle between them. If A and B creates angle θ then, . = AB . Properties of dot product: (i) . = BA = AB = . [dot […]
Explore More3D representation of a vector
Representation of a vector by coordinates: Let us consider, OX, OY and OZ are three perpendicular axes, where O is the origin. Let P is a point with coordinates (x, y, z) and = is the position vector of P. , and are the unit vectors along + ve X, Y and Z axes. Let […]
Explore MoreResolution of vector
Resolution of a vector into its components is the process to determining a set of vectors, whose resultant is the given vector. Each vector in that set is called a component of the given vector. Prove: Let us consider (= ) is resolute along the line OA and OB creates angles and with OC respectively. […]
Explore MoreVector addition and subtraction
Vector addition and subtraction problems can be solved by triangle and parallelogram law. Triangle law of vector addition: Statement: If two vectors are represented both in magnitude and direction by two sides of a triangle taken in the same order, then the resultant of these vectors is represented both in magnitude and direction by the […]
Explore MoreClassification of vector:
Vector can be classified in various types. Such types are given below. 1. Polar vectors: The vector which has an initial point or a point of application is known as polar vector. Example: displacement, force etc. Axial vector: The vector which represents the rotational effect and act along the axis of rotation in accordance with […]
Explore More
