# a challenge for targetiitians

let a,b,c,d represent coplanar vectors and sin(A)a + 2sin(2B)b + 3sin(3C)c - 4d = 0 then find the least value of sin(A)^2 +sin(2B)^2 + sin(3C)^2 is....

1. 7/8
2. 8/7
3. 1
4. 2/3

• Rohan Ghosh ·

well in my first answer i included that ..

but 0 can be the minimum

just take a=b=c=i^ and d=0

they are coplanar .... :)

• Charan Reddy ·

8/7 is the correct answer..isn't it?

• Mayank Sharma ·

Guys,i help u in this question.myself faculty of maths,bansal classes..firstly by condition of coplanarity u have to get sum of coefficients is equal to zero.so value of sinA+2sin2B+3sin3C=4,after that u can assume two vectors in form of i^+2j^+3k^and sinA i^+sin2B j^+sin3C k^and now apply cauchey swartz inequality in it.u will find result directly..answer is 8/7..thankx.

• Rohan Ghosh ·

i ve already given an answer i think this is it ..

• deepanshu001 agarwal ·

yaar d is a vector representing a point and using coplanarity theorem

and finally i dint mak the ques ....

FIITJEE guys gav it in one of the AITS last year....

• Rohan Ghosh ·

16|d|2/(|a|2+4|b|2+9|c|2)

• Rohan Ghosh ·

and further the answer i got is by application of coplanarity and a little bit of cauchy schwarz law ...

• Rohan Ghosh ·

hey how come you are getting 4 there!!!!

havent i mantioned d=0!

• Mani Pal Singh ·

EXPLAIN#12

• deepanshu001 agarwal ·

read post 18 how can 3 0 zeroes be added to giv u a 4

• Rohan Ghosh ·

cant sinA sin2B sin3C be all zero???

when d=0 and a,b,c=i^ we get

sinA + 2sin2B + 3sin3C =0

also observe that the quantity given to be found out >=0

here sin2a sin2b sin3c if all zero agrees with the above eqn and also gives the minimum possible value of this =0 ...!!

• deepanshu001 agarwal ·

u guys r not readin the ques properly

ye bhi to dekho ki minimum value nikalni kiski hai ..\

mr . rohan wat u ve found out is the minimum value of sin(A) + 2sin(2B) + 3sin(3C)

thats not mah ques...

• Rohan Ghosh ·

Hey deepansh ..

a,b,c =i^ are coplanar!!!!

and further there is no relation between a,b,c, and d!!!
we can indeed have a minimum value

• deepanshu001 agarwal ·

no rohan u r not on the ryt track

wat i was able to do was....

Using coplanarity theorem of vectors....

sin(A) + 2sin(2B) + 3sin(3C) = 4

nao wat.....?

• Mani Pal Singh ·

@DEEP U R AN OVERSMART GUY
THRE IS NO OPTION 0 AVAILABLE AND UR QUES WAS NOT CLEAR

MR CHALLANGER

• skygirl ·

tum hi karlo naa yeh question....

tum bhi toh targetiit-an hi ho 

• deepanshu001 agarwal ·

yes rohans ryt .....

my ques is complete ,,, this is ol dat is given

• Mani Pal Singh ·

COPLANAR IS MEANT TO BE TAKEN CARE OFF!!!!!!!!!

• Rohan Ghosh ·

i am not getting it as a value

but as 16|d|2/(|a|2+4|b|2+9|c|2)

and as metal mentioned if there is no restriction choose d=0 min=0

• Mani Pal Singh ·

MR ROHAN then can u please explain wat r A,B,C???

• Rohan Ghosh ·

well we require the minimum value ...

• metal ·

The question is not clear. Are Sin(A), Sin(B), Sin(C) independent of vectors a,b,c and d?
If that's so, here's my answer:-

Let me choose the vectors such that a+2b+3c-4d=0

Then Sin(A) = Sin(B)= Sin(C)=1, and maximum value=3.

• Mani Pal Singh ·

@deepanshu

A,B,C,D r the angles between what???
make the question more clearer

• deepanshu001 agarwal ·

if no 1 s gettin it then i hv a soln .
which i m unable to understand it....
if u guys want dt then i can do that.....

• deepanshu001 agarwal ·

nao i hv posted the options above
tak a luk......

• deepanshu001 agarwal ·

try it out ppl....

• deepanshu001 agarwal ·

no.... i m sry dts not d ans

• Manas ·

he wats the answer .is it 4/3?????

• MATRIX ·

hahaha.............

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