Advanced level vector
Vector triple product: 1. ( ) = (.) – (.) 2. ( ×) × = – ×( ×) = – [(.) – (.)] = (.) – (.) 3. (×).(×)×(×) = (.×)² Prove: Let, × = so, (×)×(×) = ×(×) = (.) – (.) = (×.) – (×.) = (.×) – (.×) = ( […]
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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, for a triangle, the ratio of one side with the […]
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Definition 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. […]
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Vector cross product is used to calculate area of triangle, rectangle or parallelogram. We can calculate moment of force or torque using cross product of vector. 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 […]
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Vector dot product
Vector dot product or scalar product: The dot or 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 […]
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3D representation of vector
We can use 3D representation of a vector to calculate position vector of a point. Angle of vector with given axis can be calculated by 3D representation of vector also. 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 […]
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Resolution 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 resoluted along the line OA and OB creates angles and respectively. From point […]
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Vector 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 […]
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Classification 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 […]
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