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Two vector quantities can be combined into a scalar quantity because a vector lives in a vector space, which requires the existence of an operation called the dot product (also commonly known as the scalar product or inner product).
The exact form of this operation depends on the type of vector space, and of course one can define other operations which map two vectors into a scalar.
A commonly used definition is as follows:
Imagine vector one contains these values (x1, x2, x3, x4) and vector two contains these values (y1, y2, y3, y4), the dot product would turn this into:
x1*y1 + x2*y2 + x3*y3 + x4*y4
The dot product gives a measure of the angle between two vectors and is often used as such in for example mechanics.
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Which are the scalar quantities?
A scalar quantity is a non-vector quantity. In a vector quantity, direction is relevant. In a scalar quantity, it is not. For example, mass (measured in kg.) is a scalar; force is usually indicated as a vector (magnitude in Newton, but the direction is also relevant).A scalar quantity is a non-vector quantity. In a vector quantity, direction is relevant. In a scalar quantity, it is not. For example, mass (measured in kg.) is a scalar; force is usually indicated as a vector (magnitude in Newton, but the direction is also relevant).A scalar quantity is a non-vector quantity. In a vector quantity, direction is relevant. In a scalar quantity, it is not. For example, mass (measured in kg.) is a scalar; force is usually indicated as a vector (magnitude in Newton, but the direction is also relevant).A scalar quantity is a non-vector quantity. In a vector quantity, direction is relevant. In a scalar quantity, it is not. For example, mass (measured in kg.) is a scalar; force is usually indicated as a vector (magnitude in Newton, but the direction is also relevant).
Is scalar quantiy is added with vector quantity?
A scalar quantity added to a vector quantity is a complex quantity. An example is a complex number z = a + ib, a is the scalar and ib is the vector quantity.If the vector quantity is 3 dimensional, ib + jc + kd, then the scalar and vector forms a quaternion quantity.
A vector quantity has direction a scalar quantity does not true or false?
True. A vector quantity has both magnitude and direction, while a scalar quantity only has magnitude.
What is the difference between vector and scalar quantities?
Vector quantity is a quantity characterized by magnitude and direction.Whereas,Scalar quantity is a quantity that does not depend on direction.
Is temperature a scalar quantity or vector quantity?
temperature is a scalar quantity................
Distinguish between scalar and vector quantity?
A scalar is just a number. A vector is a row or column of numbers. For example: 6 is a scalar while (1, 0, 23.5) is a vector.
Is temperature vector or scalar?
Temperature is a scalar quantity. It has magnitude but not direction.
Is length a scalar quantity or a vector quantity?
length is a scalar quantity buddy . but displacement is vector quantity. Length is a vector quantity If it is associated with direction.. Because having direction make it vector... S0 being vector or scalar depends upon how and where it is used..
Why cant a vector quantity be added to a scalar quantity?
vector quantity is magnitute and direction scalar is magnitute only
Is the following measurement a vector quantity or a scalar quantity?
A vector quantity.
Is the work vector quantity or scalar quantity?
Work is a scalar quantity.
Is heat transfer a scalar quantity or vector quantity?
A vector
