If `|(x^k,x^(k+2),x^(k+3)), (y^k,y^(k+2),y^(k+3)), (z^k,z^(k+2),z^(k+3))|=(x-y)(y-z)(z-x){1/x+1/y+1/z}` then `k=`

det [[x ^ (k), x ^ (k + 2), x ^ (k + 3) y ^ (k), y ^ (k + 2), y ^ (k + 3) z ^ (k) , z ^ (k + 2), z ^ (k + 3)]] = (xy) (yz) (zx) {(1) / (x) + (1) / (y) + (1) / ( from)}

Let x gt 0 , y gt 0 , z gt 0 are respectively the 2^(nd) , 3^(rd) , 4^(th) terms of a G.P. and Delta=|{:(x^(k),x^(k+1),x^(k+2)),(y^(k),y^(k+1),y^(k+2)),(z^(k),z^(k+1),z^(k+2)):}|=(r-1)^(2)(1-(1)/(r^(2))) (where r is the common ratio), then

If quad f(x)=((x-a)(x-b))/(x) and ((f(z))/((z-x)(z-y))+((f(y))/((y-z)(y-x))+((f(z))/((z-x)(z-y))=(k)/(xyz)) then k=

If |(x+y,y+z,z+x),(y+z, z+x,x+y),(z+x,x+y,y+z)| =k |(x,z,y),(y,x,z),(z,y,x)| , then k is equal to

z=x+iy,z^(1/3)=a-ib,(x)/(a)-(y)/(b)=k(a^(2)-b^(2)) then k is :

(x-k)/1=(y-2)/2=(z-3)/1, (x+1)/1=(y+2)/2=(z+3)/1 coplanar then find k

If the lines (x)/(1)=(y)/(2)=(z)/(3), (x-k)/(3)=(y-3)/(-1)=(z-4)/(h) and (2x+1)/(3)=(y-1)/(1)=(z-2)/(1) are concurrent, then the value of 2h-3k is equal to

if the lines (x - 1)/(-3) = ( y - 2)/(2k) = ( z -3)/(2) and (x -1) /(3k) = ( y - 5)/(1) = (z - 6 ) /(-5) are at night angle , then find the value of k .

If a^(x) = b , b^(y) = c, c^(z) = a, x = log_(b) a^(k_(1)) , y = log_(c)b^(k_(2)), z = log _(a) c^(k_(3)), , then find K_(1) K_(2) K_(3) .