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Why is it necessary to use the trig function cosine when working with vectors?
The cosine function is used to determine the x component of the vector. The sine function is used to determine the y component. Consider a vector drawn on an x-y plane with its initial point at (0,0). If L is the magnitude of the vector and theta is the angle from the positive x axis to the vector, then the x component of the vector is L * cos(theta) and the y component is L * sin(theta).
What is the magnitude of vector -2 0?
A vector, starting at the origin and going to point (-2,0):Since there is no y-component, the magnitude is the absolute value of the x componentmagnitude = 2magnitude of a vector = sqrt( X2 + Y2) = sqrt ((-2)2 + 02) = sqrt(4) = 2where X & Y are the x-component & y-component of the vector.
How can you find a unit vector in the same direction as the given vector?
Divide the vector by it's length (magnitude).
Where is the second vector's tail placed when two vectors are added graphically using the tip to tail method?
it is placed at the tip of the first vector
How does vector calculus applies to electromagnetism?
Vectors are directional numbers. Calculus determines changes. Electromagnetism involves directional fields and thus vector calculus is the tool to calculate the changes in directional fields.The training in Mathematics and Physics is deficient in that Nature involves the combination of real and vector numbers called Quaternions. Quaternions were invented by William Rowan Hamilton in 1843. Quaternions consist of a real number r and three vectors (i,j,k) such that i2 = j2 = k2 = ijk = -1.A quaternion point is p=r + ix +jy + kz= r + v where v is the vector part.Quaternion calculus has a derivative I call X for Khepra which consists of Hamilton's vector derivative called Del = id/dx + j d/dy + kd/dz and a real derivative d/dr = d/cdt .X= d/dr + Del = d/dr + id/dx + jd/dy + kd/dz = d/cdt + Del = [d/dr,Del]Using this quaternion derivative the fundamental laws of electromagnetism can be derived as th Boundary Condition, 0= XE where E is the quaternion electric field E=Er + Ev = [Er,Ev].The First Derivative of the Electric field isXE= (dEr/cdt - Del.Ev) + (dEv/cdt + DelxEv + Del Er)The Equilibrium Condition for the Electric field occurs when the the First Derivative is set to zero:0=XE= (dBr/dt - Del.Ev) + (dBv/dt + Del Er)This is the Quaternion Equilibrium Condition Equation, notice that the Curl Term DelxEv =0 and is not in the equation. The curl is zero at Equilibrium and the remaining vector terms are "Equal and Opposite"! Equilibrium requires that the sum of the reals and vectors sum to zero. The vectors cannot sum to zero unless DelxEv=0, this happens only when the other terms are parallel or anti-parallel. Equilibrium is the anti-parallel case, thus Newton's "Equal and Opposite" Rule in his 3rd law of Motion.This Equilibrium Condition is the Stationary and Invariant Condition and the Cauchy-Riemann Continutiy Condition.Maxwell's EquationsdBr/dt - Del.Ev=0dBv/dt + DelxEv=0are incorrect in including DelxEv, it should be Del Er. DelxEv is perpendicular to dBv/dt =dEv/cdt. Vector Calculus shows DelxEv is perpendicular to dEv/dr, thus the sum of orthogonal vectors is not zero unless both vectors are zero.This shows that Maxwell's Equations are incorrect and the proper Electromagnetism Equations are derived by Quaternion Calculus.
Vector component greater than the vectors magnitude?
A vector component can never be greater than the vector's magnitude. The magnitude of a vector is the length of the vector and is always greater than or equal to any of its individual components.
Can a vector have a component greater than vectors magnitude?
No.
Can a vector have a component greater than the magnitude of vector?
no a vector cannot have a component greater than the magnitude of vector
Can a vector have a component greater than the vector's magnitude?
No, a vector's component cannot be greater than the vector's magnitude. The magnitude represents the maximum possible magnitude of a component in any direction.
Can a vector have a component greater than the magnitude of the vector?
No, a vector component is a projection of the vector onto a specific direction. It cannot have a magnitude greater than the magnitude of the vector itself.
Can a component of vector greater than vector magnitude?
No, a component of a vector cannot be greater than the magnitude of the vector itself. The magnitude of a vector is the maximum possible value that can be obtained from its components.
Can the magnitude of the difference between two vectors ever be greater than the magnitude of either vector?
Yes, the magnitude of the difference between two vectors can be greater than the magnitude of either vector. This can occur when the vectors are in opposite directions or have different magnitudes such that the resulting difference vector is longer than either of the original vectors.
Can the component of a vector ever be greater than the magnitude of the vector?
No.
Can a vector have a component greater than it magnitude?
No.
Can a vector have a component greater than the magnitude?
No.
Can the magnitude of a resultant vector be greater than the sum of individual vectors?
The resultant vector IS the sum of the individual vectors. Its magnitudecan be the sum of their individual magnitudes or less, but not greater.
Can a vector have a component greater than its magnitude?
No a vector may not have a component greater than its magnitude. When dealing with highschool phyics problems, the magnitude is usually the sum of two or more components and one component will offset the other, causing the magnitude to be less then its component
