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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.
Multiplication Rule: Dependent Events The joint probability of two events A and B which are dependent is equal to the probability of A multiplied by the probability of B given
to plot (5,-4), start at (0,0) and move 5 units left and 4 units down
Consider the clique graph below. a) How many subgraphs of G with 3 nodes are there? b) How many of the subgraphs defined in part(a) are induced subgraphs?
Sally gets paid x dollars per hour for a 40-hour work week and y dollars for every hour she works over 40 hours. How much did Sally earn if she worked 48 hours? Since she worke
1+1
If tanx+secx=sqr rt 3, 0 Ans) sec 2 x=(√3-tanx) 2 1+tan 2 x=3+tan 2 x-2√3tanx 2√3tanx=2 tanx=1/√3 x=30degree
the length of three pieces of ropes are 140cm,150cm and 200cm.what is the greatest possible length to measure the given pieces of a rope?
Solve the subsequent IVP. cos(x) y' + sin(x) y = 2 cos 3 (x) sin(x) - 1 y(p/4) = 3√2, 0 Solution : Rewrite the differential equation to determine the coefficient of t
Mrs. Farrell's class has 26 students. Just 21 were present on Monday. How many were absent? Subtract the number of students present from the total number within the class to de
Data entry is performed in 2-person teams. Each 2-person team can enter 520 surveys per day. A selection of 7540 surveys must be entered by day''s end. How many total employees, wo
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