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Let P_(1): x+y+z=0 P_(2)x+2y+3y=0 P_(3): x+3y+5z=0 be three planes L_(1) is theline of intersection of P_(1) & P_(2) LetP(2,1-1) be point on P_(3) If (alpha,beta,lambda) is image of point P in line L_(1) then value of|alpha + beta+ lambda| is

Answer»


Solution :Direction RATIO of line `L_(1)` is `|(HAT(i),hat(j),hat(k)),(1,1,1),(1,2,3)|`
therefore Line `L_(1):(X)/(1)=(y)/(-2)=(z)/(1)`

`(LAMBDA-2)-2(-2lambda-1)+(lambda+1)1=0`
`6lambda=-1implies lambda=(-1)/(6)`
`(alpha+2)/(2)=lambda,(beta+1)/(2)=-2lambda,(lambda-1)/(2)=lambda`
`implies alpha+beta+lambda=-2-1+1+2lambda-41+2lambda=-2`


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