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The angles between three non-zero and non coplanar vectors a,b and c are α between b and cand β between c and aand γ between a and b.The vector u and v are defined by u=(aXb)Xc;v=aX(bXc).If u is perpendicular to v, then show that eithera is perpendicular to cor cosβ=cosα.cosγ . solution) Given that u=(axb)xc, v=ax(bxc), both the vectors are equal in magnitude because of the associated law, and u.v=0, therefore it must be true that a.c=0, because excluding a and c , b is not situated at right angles so angle between a and c is 90.
Use green's theorem to computer the integral F . dr where F = ( y^2 + x, y^2 + y) and c is bounded below the curve y= - cos(x),, above by y = sin(x) to the left by x=0 and to the r
The frequency of oscillation of an object suspended on a spring depends on the stiffness k of the spring (called the spring constant) and the mass m of the object. If the spring is
a car comes to a stop from a speed of 30m/s in a distance of 804m. The driver brakes so as to produce a decelration of 1/2m per sec sqaured to begin withand then brakes harder to p
A circular pool is filling along with water. Supposing the water level will be 4 ft deep and the diameter is 20 ft, what is the volume of the water required to fill the pool? (π =
Find the normalized differential equation which has {x, xex} as its fundamental set
how do you work out algebra
is 4x-9 a polynomial function?
Basic indefinite integrals The first integral which we'll look at is the integral of a power of x. ∫x n dx = (x n +1 / n + 1)+ c, n
Shane rolls a die numbered 1 by 6. What is the probability Shane rolls a 5? From 2:15 P.M. to 4:15 P.M. is 2 hours. After that, from 4:15 P.M. to 4:45 P.M. is another half hour
Standard Basis Vectors The vector that is, i = (1, 0,0) is called a standard basis vector. In three dimensional (3D) space there are three standard basis vectors, i → = (1
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