Given a non-zero vector a, a unit vector u (vector of length one) in the same direction as the vector a can be constructed by multiplying a by the scalar quantity 1/|a|, that is, forming u=1|a|a=a|a| The dot product of two vectors gives a scalar that is computed in the fol...
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In free space these constants are related to the speed of light c by the relation μ0ϵ0c2 = 1. Taking the divergence of the Ampere equation (1) and using the Gauss law (3), we obtain (5)∂ρ∂t+divJ=0. This is the so-called continuity equation, which is a compatibility...
The lesson explores the product of a vector by a scalar, the dot or scalar product, and the cross product. Formulas, examples, properties, and...
equation of purity P for crystals produced from a continuous mixed-suspension, mixed-product-removal (CMSMPR) crystallizer at steady state is successfully derived as: P = 100 multiplied by (1 - 4k center dot G center dot tau/rho//C center dot k//v + 4k center dot G center dot tau)....
Find the cross product of the two vectors 3. Substitute one point into the Cartesian equation to solve ford. Example Find the equation of the plane that passes through the pointsA=1,1,1,B=−1,1,0,C=2,0,3. ...
Fortunately, multiplying the identity matrix I by λ fixes our problem as the product is itself a square matrix. So we need to solve (A−λI)v→=0→ for λ, and those will be our eigenvalues of the matrix A. Well, our only hope of systematically finding all λ requires that we ...
Find the vector equation of the following plane in product form vecr =... 03:34 Show that the line joining the origin to the point (2,1,1) is perpe... 03:49 If l(1), m(1), n(1) and l(2),m(2),n(2) are the direction cosines of tw... 02:32 Find the angle between ...
Given a nonlinearityand set, we are interested to seek for multiple solutionsof the nonlocal equation (1.1) where,andis the Riesz potential defined by heredenotes the space of radially symmetric Sobolev functions. We aim to analyze the two cases:is a fixed positive constant oris unknown and th...
Examining enzyme kinetics is critical for understanding cellular systems and for using enzymes in industry. The Michaelis-Menten equation has been widely used for over a century to estimate the enzyme kinetic parameters from reaction progress curves of s