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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.
The width of a rectangle is 30.5% of its length l. Write a formula for the area and perimeter of the rectangle in terms of l only
Equivalent or Equal sets Two sets C and D are said to be equal whether every member of set C belongs to D and every member of set D belongs also to C.
Monotonic, Upper bound and lower bound Given any sequence {a n } we have the following terminology: 1. We call or denote the sequence increasing if a n n+1 for every n.
Evaluate following limits. Solution : Let's do the first limit & in this case it sees like we will factor a z 3 out of the numerator and denominator both. Remember that
simplify the expression 3/5/64
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Confidence Interval The interval estimate or a 'confidence interval' consists of a range as an upper confidence limit and lower confidence limit whether we are confident that a
Solve the subsequent IVP. y′′ + 11y′ + 24 y = 0 y (0) =0 y′ (0)=-7 Solution The characteristic equation is as r 2 +11r + 24 = 0 ( r + 8) ( r + 3) = 0
Suggest me the solution: Consider the given universal set T and its subjects C, D and E T = {0, 2, 4, 6, 8, 10, 12} C = {4, 8,} D = {10, 2, 0} E = {0} Find out
how can i evaluate this lim of x as x approaches to a
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