IIT JEE , AIEEE Forum - Mathematics , Vectors

rat

a straight line 'l' cuts the lines AB, AC, AD of a parallelogram at B1 C1 D1 respectively. if AB₁=

₁AB AD₁=

₂AD AC₁=

₃AC then prove that 1/

₃=1/

₁ + 1/

₂ .

Anjishnu

Hello! Experts please help!!!!!!!!

amar.gupta

Dear,

let A be the origin and AB1 represent b^->(b),AC1 represent c^->(c),AD1 represent d^->(d)
but AC₁=

₃AC hence vector(AC) = (AC) c/AC1 =c/

₃similarly: vector (AB)=vector(AB1)/

1=b/

1

and : vector (AD)=vector(AD1)/

2=d/

2

then law of parallelogram : vector(AC)=vector(AB)+vector(AD)

hence: c/

3 = b/

2 + d/

1

or b/

2 + d/

1- c/

3 =0.......[1]

now since b,c,d are collinear vectors.

so according to law we can write : lb+mc+nd=0 ,where l+m+n =0 and l,m,n are scalars.

hence from [1]: 1/

2+1/

1-1/

3=0

or 1/

2+1/

1=1/

3

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