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What is the dot product of two perpendicular vectors vector a and vector b respectively?
Wiki User
∙ 6y ago
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
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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,
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoIt is zero.
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A vedtor which is perpendicular to every vector?
The zero vector is not perpendicular to all vectors, but it is orthogonal to all vectors.
How to you find a vector parallel to two given vectors?
I think you meant to ask for finding a perpendicular vector, rather than parallel. If that is the case, the cross product of two non-parallel vectors will produce a vector which is perpendicular to both of them, unless they are parallel, which the cross product = 0. (a zero vector)
When sum and difference vector of two vectors are perpendicular .are the vectors too perpendicular?
Yes.
How do you do cross products?
You need to know that the cross product of two vectors is a vector perpendicular to both vectors. It is defined only in 3 space. The formula to find the cross product of vector a (vector a=[a1,a2,a3]) and vector b (vector b=[b1,b2,b3]) is: vector a x vector b = [a2b3-a3b2,a3b1-a1b3,a1b2-a2b1]
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.
Which are the three vectors that act along the mutually perpendicular direction?
cross product of tow vector result in a vector which is perpendicular the multiplying vector then these three vector are perpedicular
A vedtor which is perpendicular to every vector?
The zero vector is not perpendicular to all vectors, but it is orthogonal to all vectors.
How to you find a vector parallel to two given vectors?
I think you meant to ask for finding a perpendicular vector, rather than parallel. If that is the case, the cross product of two non-parallel vectors will produce a vector which is perpendicular to both of them, unless they are parallel, which the cross product = 0. (a zero vector)
What is the algebraic definition of a cross product?
Cross product also known as vector product can best be described as a binary operation on two vectors in a three-dimensional space. The created vector is perpendicular to both of the multiplied vectors.
When sum and difference vector of two vectors are perpendicular .are the vectors too perpendicular?
Yes.
Dot product of unit vectors of cartesian and cylindrical coordinate system?
Unit vectors are perpendicular. Their dot product is zero. That means that no unit vector has any component that is parallel to another unit vector.
Cross product is not difine in two space why?
When performing the cross product of two vectors (vector A and vector B), one of the properites of the resultant vector C is that it is perpendicular to both vectors A & B. In two dimensional space, this is not possible, because the resultant vector will be perpendicular to the plane that A & B reside in. Using the (i,j,k) unit vector notation, you could add a 0*k to each vector when doing the cross product, and the resultant vector will have zeros for the i & jcomponents, and only have k components.Two vectors define a plane, and their cross product is always a vector along the normal to that plane, so the three vectors cannot lie in a 2D space which is a plane.
What is the product of vector and scalar?
The scalar product of two perpendicular vectors is zero.In classical mechanics we define the scalar product between two vector a and b as:a · b = |a| |b| cos(alpha)where |a| is the modulus of vector a and alpha is the angle between vectors a and b.If two vectors are perpendicular, alpha equals 90º (or PI/2 rad) and cosine of alpha is, consequently, zero.So finally a · b = 0.
How do you do cross products?
You need to know that the cross product of two vectors is a vector perpendicular to both vectors. It is defined only in 3 space. The formula to find the cross product of vector a (vector a=[a1,a2,a3]) and vector b (vector b=[b1,b2,b3]) is: vector a x vector b = [a2b3-a3b2,a3b1-a1b3,a1b2-a2b1]
How do you find the component of a vector perpendicular to another vector?
The component of a vector x perpendicular to the vector y is x*y*sin(A) where A is the angle between the two vectors.
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.
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.
