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In mathematics, the dot product is an algebraic operation that takes two equal-length sequences of numbers (usually vectors) and returns a single number obtained by multiplying corresponding entries and adding up those products. The name is derived from the interpunct "â—" that is often used to designate this operation; the alternative name scalar product emphasizes the scalar result, rather than a vector result.
The principal use of this product is the inner product in a Euclidean vector space: when two vectors are expressed in an Orthonormal basis, the dot product of their coordinate vectors gives their inner product. For this geometric interpretation, scalars must be taken to be Real. The dot product can be defined in a more general field, for instance the complex number field, but many properties would be different. In three dimensional space, the dot product contrasts with the cross product, which produces a vector as result.
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What is the used of dot product and cross product in real life?
The dot-product and cross-product are used in high order physics and math when dealing with matrices or, for example, the properties of an electron (spin, orbit, etc.).
How does the magnitude of a vector relate to the dot product?
The magnitude of dot product of two vectors is equal to the product of first vector to the component of second vector in the direction of first. for ex.- A.B=ABcos@
Why is the dot product scalar?
Because only the magnitudes are multiplied.
What is dot product?
In vector calculus a dot product of two vectors is basically the product of the length of one vector and the length of the parallel component of the other; It doesn't matter which one is taken first because length is a scalar and scalars are commutative. the easiest way to determine the dot product of u and v(u•v) is to simply multiply the length of each vector together and then multiply by the cosine of the angle between them (|uv|cosӨ, because length is a scalar, the product is always a scalar). You could also identify the the component of v that is parallel to u and and multiply their lengths but it's basically the same thing (|v|cosӨ|u|).
Is the sum of the square of cross and dot products equal to the square of their product?
Your question makes no sense.... What you meant to say is:Is the sum of the square of magnitude of the cross product and the square of dot product of two vectors equal to the product of the square of their magnitudes?i.e:|A x B|2 +(A .B)2 = |A|2|B|2The answer is YES. It is called Lagrange's identity and is a special case of the Binet-Cauchy identity.(Ax B) .(Cx D)+(A.D)(B.C)=(A.C)(B.D)Where A= Cand B= D.
What is the used of dot product and cross product in real life?
The dot-product and cross-product are used in high order physics and math when dealing with matrices or, for example, the properties of an electron (spin, orbit, etc.).
What is vector dot product?
The dot-product of two vectors is the product of their magnitudes multiplied by the cosine of the angle between them. The dot-product is a scalar quantity.
Is triple dot product defined?
If by "triple dot product" you mean u·v·w, then no, because that would imply the existence of a dot product between a vector and a scalar.
What are the applications of cross product and dot product in physics?
cross: torque dot: work
Is there any direction associated with the dot product of two vectors?
No. The dot product is also called the scalar product and therein lies the clue.
Why in dot product you use cos and in vector product sin?
We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.
What is the angle in which the dot product of two non zero vectors is equal?
It depends on what the dot product is meant to be equal to.
Dot product is?
Dot product is an algebraic operation when two equal-length sequences of numbers are returned as a single number.
Scalar or dot product?
They are the same.
in what components dot and cross product resolve?
A dot product is a scalar product so it is a single number with only one component. A cross product or vector product is a vector which has three components like the original vectors.
What is dot products and give some examples?
A Dot product is a very useful tool in both mechanics and 3D graphics. It calculates the cosine of the angle between two vectors.In two-dimensional space, the dot product of vectors [a, b] and [c, d] is ac + bd.Mechanical work is the dot product of force and displacement vectors.Magnetic flux is the dot product of the magnetic field and the area vectors.
Why we use sine angle in cross product while cos angle in dot product?
Because in dot product we take projection fashion and that is why we used cos and similar in cross product we used sin
