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If the planes bx-ay=n, cy-bz=l, az-cx=m, intersect In a line then al+bm+cn is equal to

If the planes bx-ay=n, cy-bz=l, az-cx=m, intersect  
In a line then al+bm+cn  is equal to
 

Grade:12

1 Answers

Aditya Gupta
2081 Points
5 years ago
we know that any plane P3 passing through the line of intersection of two planes P1 and P2 is always of the form
P3: P1+λP2=0
so, here let P1: bx-ay – n=0
P2: cy-bz – l=0
and P3: az-cx – m=0
now, P3 can also be written as
bx-ay – n + λ(cy-bz – l)=0
or P3: bx + (cλ – a)y – bλz – n – λl = 0
but in P3, coeff of y is given to be zero. so cλ – a=0
or λ=a/c
also, b= – c
 – bλ=a or a+ba/c=0
and n+λl=m or n+al/c=m
or nc+al=mc= –mb
or al+mb+cn=0

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