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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.
pythagoras theorem
if theta is a positive acute angle and 2sin theta +15cos square theta=7 then find the value of cot theta
prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.
to difine trigonometric ratios of an angle,is it necessary that the initial ray of the angle must be positive x-axis?
Sales price of a compact disc player is $200, each new cd is on sale for $12. kyle purchases a player and some cds for $224. how many cds were purchased?
how to find x,y and z in parallelograms,rhombus etc.
Comparison - the difference between two groups or numbers, namely, how much one is greater than the other, how much more is in one group than in the other. (e.g., if Munna has
Describe Adding and Subtracting Fractions in details? To add or subtract fractions, here are some steps: 1. Find the lowest common denominator (LCD) or any common denominato
Derive the probability distribution of the completion times: a. The following probability distributions relate to the completion times, in weeks, T A and T B of two independ
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