plane given is `3x+2y – 2z + 17=0`
`3x+2y-2z+c=0-> (3,8,2)`
`9+16-4 + c =0`
`c=-21`
so eqn of plane will be `3x + 2y-2z-21=0`
for coordinates lets the points are equal to `lamda`
so, `x=2lamda +1`
`y= 4 lamda+3`
`z= 3 lamda + 2`
putting it in eqn we get
`3(2 lamda+1) + 2(4 lamda+3) – 2( 3lamda+2) – 21=0`
`6 lamda + 3 + 8 lamda+ 6 – 6 lamda – 4 -21=0`
`E= sum_(r=1)^n(a+b) omega^(r-1)`
`= (a+b) +((2a+b) omega + (3a+b)omega^2 + (4a+b) omega^3 + …. + (na+b)omega^(n-1)`
`=b (1+ omega + omega^2 + …..+ omega^(n-1)) + a(1+ 2omega + 3omega^2 + 4 omega^3 + …. + n omega^(n-1)`
S`= 1 + 2omega + 3omega^2 + 4omega^3 + ….. + nomega^(n-2)`
S`omega= omega + 2omega^2 + 3omega^3 + …. + nomega^n`
subtracting these equations we get
so,`lamda = 2`
so points will be like
`x= 5`
`y=11`
`z=8`
now we have to find the distance from point `(3,8,2)` of point (5,11,8)
“
`E= sum_(r=1)^n(a+b) omega^(r-1)`
`= (a+b) +((2a+b) omega + (3a+b)omega^2 + (4a+b) omega^3 + …. + (na+b)omega^(n-1)`
`=b (1+ omega + omega^2 + …..+ omega^(n-1)) + a(1+ 2omega + 3omega^2 + 4 omega^3 + …. + n omega^(n-1)`
S`= 1 + 2omega + 3omega^2 + 4omega^3 + ….. + nomega^(n-2)`
S`omega= omega + 2omega^2 + 3omega^3 + …. + nomega^n`
subtracting these equations we get
`d= sqrt(4+9+36) =7`
option 1 is correct