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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.
multiply 9/19 times 95/7
The first section of a newspaper has 16 pages. Advertisements take up (3)3/8 of the pages. How many pages are not advertisements? Subtract the number of pages of advertisements
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
If r,R denote position vectors of points on the straight lines in the direction of a and b respectively, and if n is a unit vector perpendicular to both these directions, show that
11% of 56 is what number?
Your engineering department estimated the following production function. Q = 15L 2 - 0.5L 3 a. What is the marginal product of labor function, MP L ? b. What is the aver
Find and classify all the equilibrium solutions to the subsequent differential equation. y' = y 2 - y - 6 Solution First, get the equilibrium solutions. It is generally
what is the difference between North America''s part of the total population and Africa''s part
Right-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x>a without in fact letting x be a.
How to Find the range of a function ? Sigh. Students ask me this all the time. They don't want an explanation, they want a procedure. "Tell me the steps!" Unfortunately, th
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