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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.
Example : Determine the Taylor series for f(x) = e x about x=0. Solution It is probably one of the easiest functions to get the Taylor series for. We just require recallin
Example : Determine the equation of the line which passes through the point (8, 2) and is, parallel to the line given by 10 y+ 3x = -2 Solution In both of parts we are goi
A boy covered half of distance at 20km/hr and rest at 40kmlhr. calculate his average speed.
adison earned $25 mowing her neighbor''s lawn. then she loaned her friend $18, and got $50 from her grandmother for her birthday. she now has $86. how much money did adison have to
I am greater than 30 and less than 40. The sum of my digits is less than 5. who am I?
What were the two main political parties that formed in the majority of the new nations of Latin America post independence? In what ways were they different? Which party ascended t
Initial Conditions and Boundary Conditions In many problems on integration, an initial condition (y = y 0 when x = 0) or a boundary condition (y = y
Activity This activity will help you recognize the importance of some very famous numbers, as well as learn more about approximations. Directions Using the Internet, provi
Find out the area under the parametric curve given by the following parametric equations. x = 6 (θ - sin θ) y = 6 (1 - cos θ) 0 ≤ θ ≤ 2Π Solution Firstly, notice th
round to the nearest ten to estimate , 422+296
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