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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.
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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
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Integration Integration is the reversal of differentiation An integral can either be indefinite while it has no numerical value or may definite while have specific numerical v
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In an equilateral triangle 3 coins of radius 1cm each are kept along such that they touch each other and also the side of the triangle. Determine the side and area of the triangle.
A pilot is flying over a straight length of road. He determines the angles of depression of two mileposts, 5 miles apart, to be 32° and 48°. a) Find the distance of the plane f
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In a polygon no 3 diagnols are concurrent. If the total no of points of intersection are 70 ( interior ). find the no. of diagnols? Ans) Since no 3 diagonals are concurrent, There
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