Magnitude of a vector

However, the scalar magnitudes of g and/ from both antennas (G and F) are the same, because the scalar magnitude of a vector is the square root of the vector squared. Thus the following quantity is radiated into the vacuum ... 

This quantity has units of 1/length and is the magnitude of a vector known as the scattering vector. For our purpose here, it is sufficient to note that s is the yardstick used for measuring the distance between the scattering centers when the intensity of the scattered radiation of wavelength X is recorded at an angle 0 from the direction of the incident radiation. 

This was done in the previous chapter when determining the magnitude of a vector. 

A dimension in reciprocal space is a reciprocal of the dimension in real space (with a factor of unity). The magnitude of a vector d hkl in a reciprocal lattice equals the reciprocal of plane spacing (<4h) in real space. 

In the Nyquist format, the is plotted on they axis and Zreai is plotted on the x axis (Fig. 6.1a-d). The impedance magnitude, Z, for a circuit like the one shown in Fig. 6.1c is equal to the magnitude of a vector from the origin (0,0) to the point of interest (x,y) and the phase angle, (p, is given by the angle between the vector and the Zreai... 

Here, we have used the convention that vertical lines mean the length or magnitude of a vector. Equation (4.16) now becomes... 

The magnitude of a vector A is denoted by A or by A. The scalar product of a vector with itself gives the square of the magnitude of the vector ... 

If the force and the displacement are not in the same direction, they must be treated as vectors. A vector is a quantity that has both magnitude and direction. Vectors are discussed briefly in Appendix B. We denote vectors by boldface letters and denote the magnitude of a vector by the symbol for the vector between vertical bars or by the letter in plain type. The amount of work dw can be written as the scalar product of the two vectors F and dr where F is the force exerted on the object and dr is its displacement ... 

We use either of the two notations in Eq. (9.2-11) to denote the magnitude of a vector the boldface letter within vertical bars or the letter in plain type. The magnitude of a vector is always non-negative (positive or zero). 

For three orthogonal axes, v coordinates, s, q, f, are defined such that s is the magnitude of a vector in v, space, q is the elevation angle relative to the plane (q = 0 corresponds to... 

The magnitudes of a vector a and a second-order tensor x are defined by ... 

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