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
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.
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.
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.
They give us different results. The dot product produces a number, while the scalar multiplication produces a vector.
Yes, the scalar product of two vectors can be negative if the angle between them is obtuse (greater than 90 degrees). In this case, the result of the scalar product will be negative.
Yes, a scalar product can be negative if the angle between the two vectors is obtuse (greater than 90 degrees). The scalar product is the dot product of two vectors and is equal to the product of their magnitudes and the cosine of the angle between them. A negative scalar product indicates that the vectors are pointing in opposite directions.
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
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|).
They are the same.
Nothing. Multiplication is commutative and associative.Nothing. Multiplication is commutative and associative.Nothing. Multiplication is commutative and associative.Nothing. Multiplication is commutative and associative.
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.
The product of scalar and vector quantity is scalar.
No, a scalar quantity cannot be the product of two vector quantities. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. When two vectors are multiplied, the result is a vector, not a scalar.
no
The product of a vector and a scalar is a new vector whose magnitude is the product of the magnitude of the original vector and the scalar, and whose direction remains the same as the original vector if the scalar is positive or in the opposite direction if the scalar is negative.
Yes, a scalar product can be negative if the angle between the two vectors is greater than 90 degrees. In this case, the dot product of the two vectors will be negative.