If x, y, z are in arithmetic progression...

If x, y, z are in arithmetic progression with common difference d, `x ne 3d`, and the determinant of the matrix `[(3, 4sqrt(2),x),(4, 5sqrt(2),y), (5, k, z)]` is zero, then the value of `K^(2)` is:

A

6

B

72

C

36

D

12

AI Generated Solution

Similar Questions

Explore conceptually related problems

If x,y,z are in AP with common difference d and the rank of the matrix det[[5,5,x5,6,y6,k,z]] is 2, then

If abs((3,4sqrt2,x),(4,5sqrt2,y),(5,k,z))=0 and x,y,z are in A.P with common difference d , xne3d then value of k^2 is

If x^(2) + 3y^(2) + 4z^(2)+ 19 = 4 sqrt(3) ( x + y + z) , then the value of ( x - y + 4z) is:

sin57^(@)cos3^(@)=(sqrt(x)+sqrt(y)+1)/(z) , and (x+y+z)=k^(2),k in R then the value of k=

IF lines (x-1)/(2) =(y+1)/(3) =(z-1)/(4) and x-3 =(y-k) /(2) = z intersect then the value of k is

If x,y, z are in A.P., then the values of the determinant |(a +2,a +3,a + 2y),(a + 3,a +4,a + 2y),(a +4,a +5,a + 2z)| , is

If the line (x+1)/3=(y-2)/4=(z+6)/5 is parallel to the planes 2x-3y+kz=0 , then the value of k is

If x=sqrt(7)-sqrt(5),y=sqrt(5)-sqrt(3),z=sqrt(3)-sqrt(7) then find the value of x^(3)+y^(3)+z^(3)-2xyz