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# If two vectors are orthogonal then their dot product is

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In Euclidean space, **two** **vectors** **are** **orthogonal** **if** and only if their **dot** **product** **is** zero, i.e. they make an angle of 90° (π/2 radians), or one of the **vectors** **is** zero. Hence orthogonality of **vectors** **is** an extension of the concept of perpendicular **vectors** to spaces of any dimension. 3. You can also use the fact that **dot product** of **vectors** equals zero if they are perpendicular. Let u and v be as in the question and z be the perpendicular **vector**, we have system.

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The formal definition of **orthogonal** signals does not necessarily mean that they are unrelated or uncorrelated, although that is how the term is often used in casual "engineering speak.". Formally, **two** **vectors** **are** **orthogonal** **if** **their** **dot** **product** **is** zero, using the standard inner-**product** (**dot** **product**) equation for function spaces:. Definition 9.3.4. The **dot** **product** of **vectors** u = u 1, u 2, , u n.

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There are **two** ways to calculate the **dot** **product**. We are going to look at each. Option 1: Element by Element Multiplication The first option is to obtain the sum over all element by element multiplications. Let's go back to the **two** **vectors** we used in the beginning and call them a and b.

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Example 2 The **dot** **product** can be used to find out if **two** **vectors** **are** **orthogonal** (i.e they are perpendicular or their directions make 90 degrees). The geometric definition of the **dot** **product** **is** u ⋅ v = || u || || v || cos (θ) where θ is the angle between **vectors** u and v. Hence, the **dot** **product** of **two** **orthogonal** **vectors** **is** equal to zero since.

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