Without expanding at any stage, find the value of : `|{:(,a,b,c),(,a+2x, b+2y, c+2z),(,x,y,z):}|`

Without expanding at any stage, find the value of the determinant : Delta=|(20,a,b+c),(20,b,a+c),(20,c,a+b)|

Without expanding determinant at any stage evaluate |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Show that |{:(x,y,z),(2x+2a,2y+2b,2z+2c),(a,b,c):}|=0

If u=ax+by+cz , v=ay+bz+cx , w=ax+bx+cy , then the value of |{:(a,b,c),(b,c,a),(c,a,b):}|xx|{:(x,y,z),(y,z,x),(z,x,y):}| is

If a ,b ,c ,d ,e , and f are in G.P. then the value of |((a^2),(d^2),x),((b^2),(e^2),y),((c^2),(f^2),z)| depends on (A) x and y (B) x and z (C) y and z (D) independent of x ,y ,and z

If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

If x y z=0, then find the value of (a^x)^(y z)+(a^y)^(z x)+(a^z)^(x y)= (a)3 (b) 2 (c)1 (d) 0

Let a=xhati+12hatj-hatk,b=2hati+2xhatj+hatk and c=hati+hatk . If b,c,a in that order form a left handed system, then find the value of x. [x_(1)a+y_(1)b+z_(1)c,x_(2)a+y_(2)b+z_(2)c,x_(3)a+y_(3)b+z_(3)c] =|(x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)),(x_(3),y_(3),z_(3))|[abc] .