Q.2 Q.3 i solved in exam, Q.1 became too lengthy does a shortcut there Q.4 nahi bana....
Q1. A fixed Pt. P(5,2) is given and two points A and B on x=y and y=0,
Find:
i) coordinates of A for |PA+PB+PC|min
ii) coordinates of B for |PA+PB+PC|min
iii) value of |PA+PB+PC|min
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33 Answers
yup this is correct..
and the solution is very simple u can make use of it!
Q.5 (need hint)
ay-by=logxb (given)
then find the area of rectangle..... in fig.....
U have 2 find the area of the rectangle formed by y axis and three lines such that two vertices are on given graph
i think it should be such that light travels as shown after reflections....
any comments??
hey priyam any success on these?
The last one seems to be a bit tricky.. i guess i will have to give it some time..
din click on the first look :)
if u dont figure out.. do let me know. it is very easy..
btw when i post the solution of
http://targetiit.com/iit_jee_forum/posts/10th_november_2008_480.html
It will become crystal clear to u..
Right now u might be using similar triangles and crap.. then u might not need anything other than a straight line!!
:)
is the answer (29/7,29/7) on x=y
and (29/10,0) on x axis
i took the image point q of p taking x axis as mirror then took q's image r taking x=y as mirror then joined r and p which is a straight line and also the minimum distance as we know that minimum distance b/w two points is a straight line
I remember /7 in the denominator when i solved..
ur method is perfect..
I cant say the final answer cos i will nedd to check..
just tell the 2 points that u joined.. then we will be sure that u are absovlutely correct :)
good work coolspirit :)
gr8 that u got the method i was talking :)
Let s=(a.b'+a'.b)/|ab|---1
we know |ab|=|a||b|
we consider a=x+iy--2 & b=p+iq---3...
..On putttin 2 & 3 in 1 along with resp conjugates we get-----
s=2(px+qy)/√{(x2+y2)(p2+q2)}...thus s is real always...
Hence we proceed as under.....
s2=(a.b'+a'.b)2/|a|2|b|2
s2={(a.b'-a'.b)/|ab|}2+4{(aa')(bb')/|a|2|b|2}
........THE LAST STEP ABOVE IS IMP.....
now...we know aa'=|a|2....same 4 bb'....
thus now...
s2={(a.b'-a'.b)/|ab|}2+4
now subtracting any 2 diff complex num of the above exp can giv any real num other than 0....thus greatest value of the exp in braces is zero....
s2=4
......max(s)=2.......(Ans)
Q2. max value of (a.b'+a'.b)/|ab| a and b are complex no and a' means a conjugate.....
i have not tried it in test so will have 2 try....
actually paper was too fitting wala ......
Oh now i am totally messed up i will collect the question and post it later......... i don.t remember questions i solve and forget it....
no problem friend.. atleast u give good problems.. i like ur questions.. nd learn also :)
a and b are complex
aur haan din bhar 7 and half hour test dene ke baad itna galti ho jata hai
that is |PA+PB+AB|min