## Toppers Notes on Vectors

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### Table of Content

• Definition of vectors.
• Representation and notation of vectors.
• Modulus or magnitude of a vector.
• Multiplication of a vector by a scalar.
• Equal vectors, Unit vectors, Null or zero vectors.
• Collinear or parallel vectors.
• Like and unlike vectors.
• The angle between the two vectors.
• The position vector of a point.
• Component of a vector in three dimensions.
• Section formula of vectors.
• Linearly dependent and independent of the vectors.
• Collinearity of three points.
• Test of collinearity.
• Coplanarity of four points.
• Test of coplanarity.
• Scalar product and properties of the scalar product.
• Cross product or vector product and properties of the cross product.
• Scalar triple product and properties of the scalar triple product.
• Vector triple product and properties of the vector triple product.
• Reciprocal system of vectors and properties of the Reciprocal System of vectors.
• Application of the vectors in coordinate geometry.