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What are different conditions that could make vector product zero?
Wiki User
∙ 12y ago
First of all, you have to define what you mean by "vector product".
-- The "dot product" is zero if the vectors are perpendicular, regardless of their magnitudes.
-- The "cross product" is zero if the vectors are collinear or opposite, regardless of their magnitudes.
-- Perhaps when you say "product", you mean the "result" of two vectors, which
a mathematician or physicist would cal their "sum".
The sum of two vectors is zero if their magnitudes are equal and their directions
differ by 180 degrees.
An infinite number of other possibilities exist for a sum of zero, depending on the
magnitudes and directions of two vectors.
Wiki User
∙ 12y ago
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Why vector quantities are not divisible?
I'll assume you are referring to the inverse of the most common process of vector multiplication, namely the formation of an inner product, also called a scalar product or dot product, between two vectors of the same size. In this operation, vectors with, for example, components (a,b,c,d) and (e,f,g,h) must be pairwise multiplied and summed, to arrive at the scalar result ae + bf + cg + dh. Any two ordinary vectors of matching size (number of components) can be "multiplied" to get an inner product. (There is another kind of multiplication of two 3-vectors called the cross-product, which is sometimes invertible, but because the cross-product only works with two vectors in 3-space, it does not seem useful to discuss the cross-product further in the context of general vector division. Similarly, one could individually multiply the components of the two vectors to get a sort of third vector. Although that operation would be invertible under some conditions, I am not aware of any meaning, or physical significance, for the use of that technique. Since the result of taking the inner product of two vectors is a scalar, that is, a single real number, most of the information about the two vectors is lost during the computation. The only information retained by the inner product is the magnitude of the projection of one vector A onto the direction of another vector B, multiplied by the magnitude of B. But division is the inverse operation of multiplication. In a sense, division undoes the work of a previous multiplication. Since all information about the direction of each vector is discarded during the calculation of an inner product, there is not enough information remaining to uniquely invert this operation and bring back, say, vector A, knowing vector B and the value of the scalar product.
Is intensity of light scalar or vector quantity?
I think light could not be recoginzed as a vector. However, I think the light intensity could be devided into the x-y axises.
What could not be vector magnitudes?
5 hours ^_^
How could a vector be harmful to rector?
Because your mommy told it to.
What the magnitude alone of a vector quantity could be called?
scalar
A vector a is along the positive z axis and it's vector product with another vector b is zero then vector b could be?
Vector b would be along the z axis, it could have any magnitude.
Why vector division is not possible?
In the case of the dot product, you would need to find a vector which, multiplied by another vector, gives a certain real number. This vector is not uniquely defined; several different vectors could be used to give the same result, even if the other vector is specified. For the other two common multiplications defined for vector, the inverse of multiplication, i.e. the division, can be clearly defined.
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.
How do you find a normal vector?
A normal vector is a vector that is perpendicular or orthogonal to another vector. That means the angle between them is 90 degrees which also means their dot product if zero. I will denote (a,b) to mean the vector from (0,0) to (a,b) So let' look at the case of a vector in R2 first. To make it general, call the vector, V=(a,b) and to find a vector perpendicular to v, i.e a normal vector, which we call (c,d) we need ac+bd=0 So say (a,b)=(1,0), then (c,d) could equal (0,1) since their dot product is 0 Now say (a,b)=(1,1) we need c=-d so there are an infinite number of vectors that work, say (2,-2) In fact when we had (1,0) we could have pick the vector (0,100) and it is also normal So there is always an infinite number of vectors normal to any other vector. We use the term normal because the vector is perpendicular to a surface. so now we could find a vector in Rn normal to any other. There is another way to do this using the cross product. Given two vectors in a plane, their cross product is a vector normal to that plane. Which one to use? Depends on the context and sometimes both can be used!
Why vector quantities are not divisible?
I'll assume you are referring to the inverse of the most common process of vector multiplication, namely the formation of an inner product, also called a scalar product or dot product, between two vectors of the same size. In this operation, vectors with, for example, components (a,b,c,d) and (e,f,g,h) must be pairwise multiplied and summed, to arrive at the scalar result ae + bf + cg + dh. Any two ordinary vectors of matching size (number of components) can be "multiplied" to get an inner product. (There is another kind of multiplication of two 3-vectors called the cross-product, which is sometimes invertible, but because the cross-product only works with two vectors in 3-space, it does not seem useful to discuss the cross-product further in the context of general vector division. Similarly, one could individually multiply the components of the two vectors to get a sort of third vector. Although that operation would be invertible under some conditions, I am not aware of any meaning, or physical significance, for the use of that technique. Since the result of taking the inner product of two vectors is a scalar, that is, a single real number, most of the information about the two vectors is lost during the computation. The only information retained by the inner product is the magnitude of the projection of one vector A onto the direction of another vector B, multiplied by the magnitude of B. But division is the inverse operation of multiplication. In a sense, division undoes the work of a previous multiplication. Since all information about the direction of each vector is discarded during the calculation of an inner product, there is not enough information remaining to uniquely invert this operation and bring back, say, vector A, knowing vector B and the value of the scalar product.
Can a null vector be added to zero?
No, a vector cannot be added to a scalar. You could multiply a null vector by zero (and you'd get the null vector), but you can't add them.
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 intensity of light scalar or vector quantity?
I think light could not be recoginzed as a vector. However, I think the light intensity could be devided into the x-y axises.
What could not be vector magnitudes?
5 hours ^_^
When adding vector in one dimension what could the position of the head of the arrow represent?
An Arrow can be used to represent a vector by having the direction of the arrow indicate the direction of the vector and the size or length of the arrow represent the size of the vector.
How to find the area of a parallelogram with given vertices's in a 3D figure?
You need to take the magnitude of the cross-product of two position vectors. For example, if you had points A, B, C, and D, you could take the cross product of AB and BC, and then take the magnitude of the resultant vector.
What is the proper notation used to express a point in the three-dimensional coordinate plane?
It is a three dimension vector : (x, y, z). It could be either a row vector or a column vector.
