IIT JEE , AIEEE Forum - Mathematics , Vectors

patnu

if a.b=a.c & a cross b=a cross c, a is not equal to 0. then show that b=c.

harshdeep89

a.b=a.c then a.(b-c)=0

=> b=c or a is perp to b-c

aXb=aXc

then aX(b-c) =0

=> b=c or a is parallel to b-c

from the two constraints b=c

patnu

no ur wrong & a is not perp to b-c.

salonee_hs

Help please

prakhar.in

hi patnu

Harshdeep is ryt,

see first he concluded a prep to (b-c) and then he concluded a para to (b-c) which are contradictory hence his other conclusion i.e b-c=0 or b=c is proved

vishwaxlnc

no sai ur wrong forever

vasanth

hi,

a.(b-c) = 0

so

case 1a)

b = c

case1b)

a perpendicular to b-c

aX(b-c) = 0

case 2a)

b = c

case 2b)

a and b-c are parallel

case 1b) and case 2b) cannot besatisfied simultaneously, so we can rule out these cases.......so our only option is
b = c

i have given an elaborate method just to avoid confusion

harshdeep is ryt...

do rate me!

cheers~!

vineet513

u said that a.b=b.c
=> a.b=abcos A
a.c=accosA
=> abcosA= accosA
=> ab=ac
=>b=c.

u also said that a x b=a x c,
=> absinA=acsinA
=> ab=ac
=> b=c.
i think it is correct. plz rate me if i am correct

taruntanuj007

i solved this qs read my psost titled

http://www.goiit.com/posts/list/vectors-check-this-out-10501.htm#58781

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