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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 motor boat takes Six hours to cover 100 km downstream and 30 km upstream. If the motor boat goes 75 km downstream and returns back to its starting point in 8 hours, find the sp
Interpretation of r - Problems in interpreting r values A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that th
(1) Show that the conclusion of Egroff's theorem can fail if the measure of the domain E is not finite. (2) Extend the Lusin's Theorem to the case when the measure of the domain E
Determine the area of the regular octagon with the following measurements. a. 224 square units b. 112 square units c. 84 square units d. 169 square units b. See
The Video Club Martin rents movies at "regular price" andat "half price". Usually if the films are regularly priced one day, they will be at regular price the next day with probab
Formulas for the volume of this solid V = ∫ b a A ( x) dx V = ∫ d c A ( y ) dy where, A ( x ) & A ( y ) is the cross-sectional area of the solid. There are seve
Find the lesser of two consecutive positive even integers whose product is 168. Let x = the lesser even integer and let x + 2 = the greater even integer. Because product is a k
If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans : AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2
lcm method of 648
Suppose that the width of a rectangle is three feet shorter than length and that the perimeter of the rectangle is 86 feet. a) Set up an equation for the perimeter involving on
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