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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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DEVELOPING AN UNDERSTANIDNG OF MULTIPLICATION : The most important aspect of knowing multiplication is to understand what it means and where it is applied. It needs to be first i
for what value of k,the following system of equations have infinite solutions?kx + 5y -(k-5)=0;20x +ky - k=0
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Here are a few examples of some team games. The teams can be small (1-3 children) or big (15-20 children). We start with some games for small children. a) One team places a numb
Given the vectors u = 3 i - 2 j + k , v = i + 2 j - 4 k , w = -2 i + 4 j - 5 k use vector methods to answer the following: (a) Prove u , v and w can form
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Dawn wants to evaluate the volume of a basketball along with the volume of a tennis ball. Which formula will she use? The volume of a sphere is 4/3 times π times the radius cub
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