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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 boat tour company charges $11 for a harbour tour and averages 450 passengers on Saturdays. Over the past few months, the company has been experimenting with the price of a tour a
The length of the diameter of the circle which touches the X axis at the point (1,0) and passes through the point (2,3) is ? Solution) If a circle touches the x-axis, its equatio
the wholesale p of string beans in dollars per bushel and the daily supply x in thousands of bushel,are related by the equation px+6x+7p=5950. if the supply is decreasing at the r
X-intercept If an intercept crosses the x-axis we will call it as x-intercept . Y-intercept Similar, if an intercept crosses the y-axis we will call it as a y-inter
alpha and beta are concentric angles of two points A and B on the ellipse.
1. Find the third and fourth derivatives of the function Y=5x 7 +3x-6-17x -3 2. Find the Tangent to the curve Y= 5x 3 +2x-1 At the point where x = 2.
The low temperature in Anchorage, Alaska today was negative four degrees. The low temperature in Los Angeles, California was sixty-three degreees. What is the difference in the two
We now require addressing nonhomogeneous systems in brief. Both of the methods which we looked at back in the second order differential equations section can also be used now. Sin
While we first looked at mechanical vibrations we looked at a particular mass hanging on a spring with the possibility of both a damper or/and external force acting upon the mass.
Question: Classify the following differential equations as linear/nonlinear. Also, what is the order of the following differential equations? Xy'-2y =x Xy'' -2y' =xsin(y)
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