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Physical quantities having only magnitude but not associated with any direction are called scalar quantities.
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scalars are added and subtracted by algebraic method.
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Ex : Mass, speed work, power, energy, pressure etc.
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The famous triangle law can be used for the addition of vectors and this method is also called the head-to-tail method.
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As per this law, two vectors can be added together by placing them together in such a way that the first vector’s head joins the tail of the second vector.
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Thus, by joining the first vector’s tail to the head of the second vector, we can obtain the resultant vector sum.
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The resultant of scalar product/dot product of two vectors is always a scalar quantity.
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Consider two vectors a and b.The scalar product is calculated as the product of magnitudes of a, b, and cosine of the angle between these vectors.
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Scalar product = |a||b| cos α
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Here, |a| = magnitude of vector a, |b| = magnitude of vector b, α = angle between the vectors
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Physical quantities having both magnitude and direction are called as vector quantities.
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Ex : Displacement, Velocity, acceleration, force, momentum etc.
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Null Vector
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It is a vector whose magnitude is zero and direction is not specified
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Equal Vector
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Two vectors are said to be equal if they have same magnitude and direction irrespective of their initial points
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Negative Vector
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A vector with same magnitude but opposite in direction is called negative vector
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Unit Vector
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A vector whose magnitude is unity is termed as unit vector
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Parallel Vector
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If two vectors are in same direction then they are said to be parallel or like vectors.
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Position vectors
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The vector which is used to specify the position of a point 'p' with respect to some fixed point 'o' represented by OP is known as position vector of 'p' with respect to 'o'.
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Another law that can be used for the addition of vectors is the parallelogram law of the addition of vectors.
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Let’s take two vectors p and q, as shown below. They form the two adjacent sides of a parallelogram in their magnitude and direction.
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The sum p + q is represented in magnitude and direction by the diagonal of the parallelogram through their common point.
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If the product of two vectors is another vector then such a product is called vector product or cross product.
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If θ is the angle between the given two vectors A and B, then the formula for the cross product of vectors is given by:
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A × B = |A| |B| sin θ
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