1.

If the line, `(x-3)/2=(y+2)/(-1)=(z+4)/3`lies in the place, `l x+m y-z=9`, then `l^2+m^2`is equal to:(1) 26(2) 18(3) 5(4) 2

Answer» Given line is `(x-3)/2 = (y+2)/-1 = (z+4)/3`
So, point `P(3,-2,-4)` lies on the given plane `lx+my-z = 9`
`:. 3l-2m+4 = 9`
`=>3l-2m = 5->(1)`
Now, direction ratios of the line and direction ratios of the plane will be perpendicular.
So, their product is `0`.
`:.2l-m-3 = 0=>2l-m = 3->(2)`
so, multiplying (2) with `2` and subtracting it from (1),
`3l-2m-4l+2m = 5-6`
`=>l = 1`
Putting value of `l` in (2),
`2(1)-m = 3`
`=>-2-m = 3=> m = -1`
`:. l^2+m^2 = 1^2+(-1)^2 = 1+1= 2`


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