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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.
a medical clinic performs three types of medical tests that use the same machines. Tests A, B,and C take 15 minutes, 30 minutes and 1 hours respectively, with respective profits of
log6+log-4
how to do them?
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Equations of Planes Earlier we saw a couple of equations of planes. Though, none of those equations had three variables in them and were actually extensions of graphs which we
Subtraction - Vector arithmetic Computationally, subtraction is very similar. Given the vectors a → = (a 1 , a 2 , a 3 ) and b → = (b 1 , b 2 , b 3 ) the difference of the t
Maclaurin Series Before working any illustrations of Taylor Series the first requirement is to address the assumption that a Taylor Series will in fact exist for a specifi
The boundary of the shaded portion in the adjoining figure consists of our half-circles and two quarter-circles. Find the length of the boundary and the area of the shaded portion
The square of a positive number is 49. What is the number? Let x = the number. The sentence that is , "The square of a positive number is 49," translates to the equation x 2
Q. Multiplying Fractions Involving Negative Numbers? Ans. If you have only one negative sign, the result is still negative: If you have more than one, just remembe
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