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Why the product of two vectors is sometime scalar and sometime vector?
Wiki User
∙ 12y ago
Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.
This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.
Wiki User
∙ 12y ago
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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 the value of scalar product of two vectors A and B where value of vector A and B is not zero and vector product of two vectors A and B is not zero?
Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')
1 For the two vectors find the scalar product AB and the vector product?
For two vectors A and B, the scalar product is A.B= -ABcos(AB), the minus sign indicates the vectors are in the same direction when angle (AB)=0; the vector product is ABsin(AB). Vectors have the rule: i^2= j^2=k^2 = ijk= -1.
What is scalar and vector product?
The scalar product of two vectors, A and B, is a number, which is a * b * cos(alpha), where a = |A|; b = |B|; and alpha = the angle between A and B. The vector product of two vectors, A and B, is a vector, which is a * b * sin(alpha) *C, where C is unit vector orthogonal to both A and B and follows the right-hand rule (see the related link). ============================ The scalar AND vector product are the result of the multiplication of two vectors: AB = -A.B + AxB = -|AB|cos(AB) + |AB|sin(AB)UC where UC is the unit vector perpendicular to both A and B.
Why work is scalar but product of two vector?
The product of two vectors can be done in two different ways. The result of one way is another vector. The result of the other way is a scalar ... that's why that method is called the "scalar product". The way it's done is (magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them).
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.
Is it possible to multiply a vector quantity to a scalar quantity?
The product of scalar and vector quantity is scalar.
What is the value of scalar product of two vectors A and B where value of vector A and B is not zero and vector product of two vectors A and B is not zero?
Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')
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.
1 For the two vectors find the scalar product AB and the vector product?
For two vectors A and B, the scalar product is A.B= -ABcos(AB), the minus sign indicates the vectors are in the same direction when angle (AB)=0; the vector product is ABsin(AB). Vectors have the rule: i^2= j^2=k^2 = ijk= -1.
Why does the work is scalar quantity?
Work is the product of a force and a displacement. Both of those are vectors. There are two ways to multiply vectors. One of them produces another vector, the other produces a scalar. The calculation for 'work' uses the scalar product. The procedure is: (magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them).
Why the work is scalar quantity?
Work is the product of a force and a displacement. Both of those are vectors. There are two ways to multiply vectors. One of them produces another vector, the other produces a scalar. The calculation for 'work' uses the scalar product. The procedure is: (magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them).
How is the direction of the vectors involved in the definition of work?
A definition of work W: W = ⌠F∙dsWhere F is a force vector that is dot-multiplying (scalar product) the differentialdisplacement vector dS. The result is the work W, a scalar, done by the force thatproduced the displacement. But notice that the scalar product of both vectors willonly consider the force component that is collinear with the displacement vector.
What is scalar and vector product?
The scalar product of two vectors, A and B, is a number, which is a * b * cos(alpha), where a = |A|; b = |B|; and alpha = the angle between A and B. The vector product of two vectors, A and B, is a vector, which is a * b * sin(alpha) *C, where C is unit vector orthogonal to both A and B and follows the right-hand rule (see the related link). ============================ The scalar AND vector product are the result of the multiplication of two vectors: AB = -A.B + AxB = -|AB|cos(AB) + |AB|sin(AB)UC where UC is the unit vector perpendicular to both A and B.
What are the operation on vector?
That really depends on the type of vectors. Operations on regular vectors in three-dimensional space include addition, subtraction, scalar product, dot product, cross product.
Is it scalar or vector when a car stops at a stop sign?
It is neither a scalar or a vector? Scalar and vectors are used to describe quantities, for example scalars include distance and mass, while vectors include weight and velocity. We do not say that a situation is a scalar or a vector.
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.
