0
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?
Wiki User
∙ 13y ago
Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')
Wiki User
∙ 13y ago
Add your answer:
Earn +20 pts
Why CosӨ is used in dot product?
The cosine of the angle between two vectors is used in the dot product because it measures the similarity or alignment of the vectors. The dot product calculates the product of the magnitudes of the vectors and the cosine of the angle between them, resulting in a scalar value that represents the degree of alignment or correlation between the vectors.
Can scalar be a negative number?
Yes, a scalar can be a negative number. For instance: c<x₁,x₂> = <cx₁,cx₂> such that <x₁,x₂> is a vector. Let c = -1 for instance. Then, we have this vector: <-x₁,-x₂> Compared to <x₁,x₂>, <-x₁,-x₂> has negative signs. In physics and mathematics, if we multiply the vector or something by a negative value scalar, then the direction of the vector is reversed, and the magnitude stays the same. If the magnitude increases/decreases, and the direction of the vector is reversed, then we can multiply the vector by any negative non-1 scalar value.
What is the difference between unit vectors and column vectors?
a unit vector is any vector with length or absolute value 1. A column vector is any vector written in a column of since we say an mxn matrix is m rows and n columns, a column vector is mx1 matrix.
Can be magnitude of a vector have negative value?
Vectors have magnitude and direction. The magnitude is always a positive number.
What are the vector and scalar fields?
In mathematics, a field is a set with certain operators (such as addition and multiplication) defined on it and where the members of the set have certain properties. In a vector field, each member of this set has a value AND a direction associated with it. In a scalar field, there is only vaue but no direction.
What is it called when a scalar and a vector are multiplied together?
When a scalar quantity(if it has positive magnitude) is multiplies by a vector quantity the product is another vector quantity with the magnitude as the product of two vectors and the direction and dimensions same as the multiplied vector quantity e.g. MOMENTUM
Is gravity is scalar or vector quantity?
Gravity is a vector, because it is a form of acceleration (which we know by definition is a vector). Vectors hold more 'information' than scalars, because vectors are, put simply, a scalar + a direction. To help you figure out these types of questions in the future, all you have to do is figure out whether direction is an important aspect of the value in question.
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 momentum a vector?
Momentum is a vector quantity because the definition of momentum is that it is an object's mass multiplied by velocity. Velocity is a vector quantity that has direction and the mass is scalar. When you multiply a vector by a scalar, it will result in a vector quantity.
Why CosӨ is used in dot product?
The cosine of the angle between two vectors is used in the dot product because it measures the similarity or alignment of the vectors. The dot product calculates the product of the magnitudes of the vectors and the cosine of the angle between them, resulting in a scalar value that represents the degree of alignment or correlation between the vectors.
Can the magnitude of a vector have a negative value and why?
Scalars can be negative, and so can a change in a scalar value.Take temperature:You can have a temperature of -10 degrees.If temperature falls from 20 to 5 degress, the change was -15 degree.The negative value of the scalar is a consequence of where you take the "zero" to be.With speed you have to be very careful because speed is the scalar bit of velocity. Velocity with no consideration of direction.
What is vector and scalar quantities?
A vector quantity is a quantity that has both magnitude and direction. Velocity, acceleration, and force are examples of vector quantities.A scalar quantity is a quantity that has magnitude, but no direction. Time, mass, volume, and speed are examples of scalar quantities.
What is the difference between vectors and arrays?
The abstraction are the same. However, the array may be of any objects, while a vector, in narrowed definition, each element is a scalar value (e.g, int, float, double, etc), to fulfill the abs(vector) = aScalarValue property of a vector. An array with the same data type would look exactly the same. But an array of Persons will be difficult to be a vector!
Is mass a vector or scalars?
Mass is a scalar value. Scalar refers to the magnitude of the object. Vector refers to the direction. If an object is moving, it's mass is scalar and its velocity is vectorial because the velocity has a magnitude (how fast) and a direction. Hope this helps. Search Scalar and vector for the true scientific definitions.
Examples of some quantities that are scalar and vectors?
A vector has a magnitude and a direction. A scalar is only a magnitude. For example, If I say that I am going 60 m/s, that I have described my speed as a scalar value. If I say I am going 60 m/s due east, I have described both my speed and direction and therefore it is a vector.
If the equation E equals mc squared gives energy which is a scalar physical quantity how is this possible when multiplying a scalar and a vector results in a vector quantity?
Energy is a product of 1 scalar quantity which is mass and 1 vector quantity which is the velocity of light within a vacuum. The velocity of light in the equation is squared which returns an absolute value negating any sign it has. This results in both terms having no sign. A vector quantity must have both a direction and a magnitude. The product returned will always be a positive quantity which means it has no direction.
Is radius a scalar?
Yes. A scalar is a physical quantity that does not depend on direction. For example, temperature is a scalar because it has no directional value. Velocity is not a scalar (it is a vector quantity) because it has direction.
