0
i think that scalar product are commutative because the vectors are in the same direction
Wiki User
∙ 10y ago
Add your answer:
Earn +20 pts
Who is the commutative property in dot and cross product?
The cross product results in a vector quantity that follows a right hand set of vectors; commuting the first two vectors results in a vector that is the negative of the uncommuted result, ie A x B = - B x A The dot product results in a scalar quantity; its calculation involves scalar (ie normal) multiplication and is unaffected by commutation of the vectors, ie A . B = B . A
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 you only use cosine for scalar product?
That is how the scalar product is defined. Also, the projection of one vector onto another at an angle to it is directly proportional to the cosine of that angle.
Why is scalar product two vectors a scalar?
Scalar product of two vectors is a scalar as it involves only the magnitude of the two vectors multiplied by the cosine of the angle between the vectors.
What is the difference between finding the dot product and using scalar multiplication?
They give us different results. The dot product produces a number, while the scalar multiplication produces a vector.
Who is the commutative property in dot and cross product?
The cross product results in a vector quantity that follows a right hand set of vectors; commuting the first two vectors results in a vector that is the negative of the uncommuted result, ie A x B = - B x A The dot product results in a scalar quantity; its calculation involves scalar (ie normal) multiplication and is unaffected by commutation of the vectors, ie A . B = B . A
Is it possible to multiply a vector quantity to a scalar quantity?
The product of scalar and vector quantity is scalar.
Scalar or dot product?
They are the same.
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|).
What happens to the product when you change the grouping of three factors in a multiplication problem?
Nothing. Multiplication is commutative and associative.Nothing. Multiplication is commutative and associative.Nothing. Multiplication is commutative and associative.Nothing. Multiplication is commutative and associative.
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.
Can a scalar product be a negative quantity?
No,because scalar quantities have no direction. So they cant be negative
Is the following scalar product correct Answer yes or no?
no
Why you only use cosine for scalar product?
That is how the scalar product is defined. Also, the projection of one vector onto another at an angle to it is directly proportional to the cosine of that angle.
Why is scalar product two vectors a scalar?
Scalar product of two vectors is a scalar as it involves only the magnitude of the two vectors multiplied by the cosine of the angle between the vectors.
Why work done is a dot product?
As we know work done is a scalar. Also the work done is referred to as the product of force and displacement. so, we consider the dot product of force and displacement which would result in a scalar.
How do you show orthogonality of 3 unit vectors?
Showing that the scalar product between all pairs of them is equally zero.Two vector are orthogonal (or perpendicular) if the scalar product between them is zero. Lets see an example in 2D:If we have two vector, a = (a1, a2) and b = (b1,b2), ifa · b = sqrt(a1*b1 + a2*b2) = 0then a and b are orthogonal.To do the same with three vector (a, b, c) you have to show that all the combinations give zero, i.e.,a · b = a · c = b · c= 0(as the scalar product is commutative, you only need to probe this three cases).
