A is a point ( 1,3,4 ) and B is the point ( 1,-2,-1 ). A point P moves so that 3PA = 2PB find the locus of P

 hey hii zerelda iam sure i don't know the answer srry !:PP nice too meet u .. meeting after long time ... reply plhh! hoz yew ?

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ohh.....hiiii nizam.... i noe u wont noe de amswer :PP btw nyz 2 meet u toooo... hmm.. im fyn. n hope ua fyn too...:))))))

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:DDD :-o sss me tooOoo f9 zerelda ! soo btw y soo of9?! meet u some time ,,,... but don't know whennn ...??? come too school talk naa SMH !! ? i miss my old frds frm tht u r one of demm !:(((((

bye sis... tc .... fr nw meet u later !plhh reply ..... n even meet....:P

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i often cum 2 skool tok bt i neva fynd u ..ohk...bye tc..

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let P= (x,y,z), A(1,3,4), B(1,-2,-1)

given 3PA=2PB

or 9(PA)2 = 4(PB)2

9[(X-1)2+(y-3)2+(z-4)2] = 4[(X-1)2+(y+2)2+(z+1)2

9(x2+y2+z2-2x-6y-8z+1+9+16)= 4(x2+y2+z2-2x+4y+2z+1+4+1)

5x2+5y2+5z2- 18x +8x-54y-16y-72z-8z+234-24 =0

5x2+5y2+5z2-10x-70y-90z+210 = 0

x2+y2+z2-2x-35y-45z+42 =0

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thankzz...:)

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210
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Let P(x,y,z)
P divides the line segment AB in ratio 2:3
So P(x,y,z) = P([-6+26]/5 , [6-6]/5 , [9+26]/5)
                     =P(20/5 , 0/5 , 35/5)
                     =P(5,0,7)
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