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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.
Interpolation is a method of statistical estimation and the word literally means 'making insertions'. Let us consider a well-known situation whi
An electric utility company determines the monthly bill for a residential customer by adding an energy charge of 5.72 cents per kilowatt-hour to its base charge of $16.35 per month
Minimum and Maximum Values : Several applications in this chapter will revolve around minimum & maximum values of a function. Whereas we can all visualize the minimum & maximum v
If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex. [Ans: 3/2 , 3/√ 3/2 or 3/2, -3√ 3/2] Ans: OA = OB = AB OA 2 = OB 2 = AB 2
Eliminate the parameter from the subsequent set of parametric equations. X = t 2 + t Y = 2t - 1 Solution: One of the very easy ways to eliminate the parameter is to
a triangle with side lengths in the ratio 3:4:5 is inscribed in a circle
Q. How to Subtract fractions with the same denominators? Ans. Subtracting fractions is basically the same as adding them. If you don't know how to add fractions, you shoul
Connecticut state sales tax is 6%. Lucy purchases a picture frame in which costs $10.50 What is the Connecticut sales tax on this item? Find out 6% of $10.50 by multiplying $10
how can a curve be divided in three equal part?
A lobster catcher spends $12 500 per month to maintain a lobster boat. He plans to catch an average of 20 days per month during lobster season. For each day, he must allow approx
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