Table of Contents
Dot Product of Two Vectors Class 11 – Properties and Examples
Definition: The dot product of two vectors is a scalar quantity that is computed by multiplying the magnitude of one vector by the magnitude of the other vector and then adding the products of the corresponding components.
The dot product is commutative, meaning that the order of the vectors does not affect the result.
The dot product is also associative, meaning that the order of the addition of the scalars does not affect the result.
The dot product is distributive, meaning that the dot product of a vector and a scalar is the same as the scalar product of the vector and the scalar.
The dot product is symmetric, meaning that the dot product of two vectors is the same as the dot product of the reversed vectors.
The dot product is a real number.
The dot product is positive if the vectors are pointing in the same direction and negative if the vectors are pointing in opposite directions.
The dot product is zero if the vectors are perpendicular.
The dot product is used in physics to calculate the magnitude and direction of a resultant force.
The following example shows how to calculate the dot product of two vectors.
Example:
The vectors A = (4, -3) and B = (-5, 2) are given.
The magnitude of A is 4 and the magnitude of B is 5.
The dot product of A and B is 20.
Dot Product Definition
The dot product between two vectors is a scalar quantity that is calculated by multiplying the corresponding components of the vectors and then summing them. The dot product is a measure of the similarity between the vectors and is used to determine the orientation of one vector relative to another.
Dot Product Formula
The dot product of two vectors is a scalar quantity that is calculated by multiplying the magnitudes of the vectors and then multiplying the products of the corresponding components. The dot product is symbolized by the symbol “•” and is usually denoted by the letter A.
Dot Product Geometry Definition
The dot product is a measure of the similarity of two vectors. It is the product of the lengths of the vectors, multiplied by the cosine of the angle between them.
Dot Product Algebra Definition
The dot product is a mathematical operation that takes two vectors and multiplies them together to produce a scalar. The result is a number that represents the magnitude of the vector sum of the two vectors.
Properties of Dot Product of Two Vectors
The dot product of two vectors is a scalar quantity.
The dot product is commutative.
The dot product is distributive.
The dot product is associative.
The dot product is symmetric.
Dot Product of Vector-Valued Functions
A dot product of vector-valued functions is a function of one variable, defined by
(f ∗ g)(x) = f(x)g(x)
for all x in the domain of both f and g.
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