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What is the dot product of two perpendicular vectors?
zero is the answer
Can the dot product of two nonzero vectors be equal to zero?
Yes, if the dot product of two nonzero vectors v1 and v2 is nonzero, then this tells us that v1 is PERPENDICULAR to v2. :)
What is the dot product of two perpendicular vectors vector a and vector b respectively?
The dot product of two perpendicular vectors is 0. a⋅b = |ab|cos θ where: |a| = length of vector a |b| = length of vector b θ = the angle between the vectors. If the vectors are perpendicular, θ = π/2 radians → cos θ = cos(π/2) = 0 → a⋅b = |a| × |b| × 0 = 0 ----------------------------------------------------------------------------- The dot product can also be calculated for vectors of n dimensions as the sum of the products of the corresponding elements: a = (a1, a2, ..., an) b = (b1, b2, ..., bn) a⋅b = Σ ar × br for r = 1, 2 , ..., n With perpendicular vectors this sum is zero,
Can dotproduct of two vectors be negative?
The dot-product of two vectors tells about the angle between them. If the dot-product is positive, then the angle between the two vectors is between 0 and 90 degrees. When the dot-product is negative, the angle is more than 90 degrees. Therefore, the dot-product can be any value (positive, negative, or zero). For example, the dot product of the vectors and is -1*1+1*0+1*0 = -1 which is negative.
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.
What is the dot product of two perpendicular vectors?
zero is the answer
When are vectors said to be perpendicular?
Perpendicular means that the angle between the two vectors is 90 degrees - a right angle. If you have the vectors as components, just take the dot product - if the dot product is zero, that means either that the vectors are perpendicular, or that one of the vectors has a magnitude of zero.
Can the dot product of two nonzero vectors be equal to zero?
Yes, if the dot product of two nonzero vectors v1 and v2 is nonzero, then this tells us that v1 is PERPENDICULAR to v2. :)
What is the dot product of two perpendicular vectors vector a and vector b respectively?
The dot product of two perpendicular vectors is 0. a⋅b = |ab|cos θ where: |a| = length of vector a |b| = length of vector b θ = the angle between the vectors. If the vectors are perpendicular, θ = π/2 radians → cos θ = cos(π/2) = 0 → a⋅b = |a| × |b| × 0 = 0 ----------------------------------------------------------------------------- The dot product can also be calculated for vectors of n dimensions as the sum of the products of the corresponding elements: a = (a1, a2, ..., an) b = (b1, b2, ..., bn) a⋅b = Σ ar × br for r = 1, 2 , ..., n With perpendicular vectors this sum is zero,
Can dotproduct of two vectors be negative?
The dot-product of two vectors tells about the angle between them. If the dot-product is positive, then the angle between the two vectors is between 0 and 90 degrees. When the dot-product is negative, the angle is more than 90 degrees. Therefore, the dot-product can be any value (positive, negative, or zero). For example, the dot product of the vectors and is -1*1+1*0+1*0 = -1 which is negative.
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.
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.
Why CosӨ is used in dot product?
The cosine of the angle between two vectors is used in the dot product because it measures the similarity or alignment of the vectors. The dot product calculates the product of the magnitudes of the vectors and the cosine of the angle between them, resulting in a scalar value that represents the degree of alignment or correlation between the vectors.
What are the applications of cross product and dot product?
Cross product tests for parallelism and Dot product tests for perpendicularity. Cross and Dot products are used in applications involving angles between vectors. For example given two vectors A and B; The parallel product is AxB= |AB|sin(AB). If AXB=|AB|sin(AB)=0 then Angle (AB) is an even multiple of 90 degrees. This is considered a parallel condition. Cross product tests for parallelism. The perpendicular product is A.B= -|AB|cos(AB) If A.B = -|AB|cos(AB) = 0 then Angle (AB) is an odd multiple of 90 degrees. This is considered a perpendicular condition. Dot product tests for perpendicular.
What is the product of two vector quantities?
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
Why dot product of two vectors is scalar?
That's the way it is defined.
What is cross-product and dot-product?
Cross products and dot products are two operations that can be done on a pair of 2-dimensional, 3-dimensional, or n-dimensional vectors. Both can be viewed in terms of mathematics or their physical representations.The dot product of two three-dimensional vectors A= and B= is a1b1+ a2b2 + a3b3. The definition in high dimensions is completely analogous. Notice that the dot product of two vectors is a scalar, not a vector. The dot product also equals |A|*|B|cosθ, where |A| and |B| are the magnitudes of A and B, respectively and θ is the angle between the vectors. This is the same as saying that the dot product is the magnitude of one vector multiplied times the component of the second vector that is parallel to the first. Notice that this means that the dot product of two vectors is 0 if and only if they are perpendicular.The cross product is a little more complicated. In three dimensions, A × B = . Notice that this operation results in another vector. This vector always points in a direction perpendicular to both A and B, and this direction can be determined by the right-hand rule. Physically, the magnitude of this vector equals |A|*|B|sinθ, or the magnitude of the first vector times the component of the other that is perpendicular to the first. So the cross product is 0 when the vectors are parallel.
