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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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David invests $17,000 into an account and at the end of 7 years, his account has a balance of $ 26,417.77. What is the interest rate (assuming annual compounding)?
Substitution Rule for Definite Integrals Now we need to go back and revisit the substitution rule as it also applies to definite integrals. At some level there actually isn't
Sketch the graph of y = ( x -1) 2 - 4 . Solution Now, it is a parabola .Though, we haven't gotten that far yet and thus we will have to select
Suppose a regular polygon , which is an N-sided with equal side lengths S and similar angles at each corner. There is an inscribed circle to the polygon that has center C and ba
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1. Sketch the Spiral of Archimedes: r= aθ (a>0) ? 2: Sketch the hyperbolic Spiral: rθ = a (a>0) ? 3: Sketch the equiangular spiral: r=ae θ (a>0) ?
An irrigation system uses a straight 30m sprinkler pipe which is capped at one end and arranged so that all water is released directly downwards and pivots around a central point.
Introduction: In this project, you will explore a few sorting algorithms. You will also test their efficiency by both timing how long a given sorting operation takes and count
write down all the factors of 36
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