The value of |[yz, z x,x y],[ p,2p,3r],[...

The value of `|[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z` are respectively, pth, `(2q)` th, and `(3r)` th terms of an H.P. is a.`-1` b. `0` c. `1` d. none of these

Topper's Solved these Questions

DETERMINANT
CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos
DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS
CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The value of |[yz, z x,x y],[ p,2q,3r],[1, 1, 1]| , where x ,y ,z are respectively, pth, (2q) th, and (3r) th terms of an H.P. is a. -1 b. 0 c. 1 d. none of these

Find the value of the determinant |b cc a a b p q r1 1 1|,w h e r ea ,b ,a n dc are respectively, the pth, qth, and rth terms of a harmonic progression.

Find the greatest value of x^2y^3z^4 if x^2+y^2+z^2=1,w h e r ex ,y ,z are positive.

If the pth, qth, rth, and sth terms of an A.P. are in G.P., then p-q ,q-r ,r-s are in a. A.P. b. G.P. c. H.P. d. none of these

If the pth, qth, rth, and sth terms of an A.P. are in G.P., t hen p-q ,q-r ,r-s are in a. A.P. b. G.P. c. H.P. d. none of these

If x ,y ,a n dz are pth, qth, and rth terms, respectively, of an A.P. nd also of a G.P., then x^(y-z)y^(z-x)z^(x-y) is equal to x y z b. 0 c. 1 d. none of these

If a,b,c be the pth, qth and rth terms respectively of a H.P., the |(bc,p,1),(ca,q,1),(ab,r,1)|= (A) 0 (B) 1 (C) -1 (D) none of these

Given a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z are not all zero, then the value of a b+b c+c a is a. 0 b. 1 c. -1"" d. none of these

If x ,y ,a n dz are pth, qth, and rth terms, respectively, of an A.P. nd also of a G.P., then x^(y-z)y^(z-x)z^(x-y) is equal to a. x y z b. 0 c. 1 d. none of these

CENGAGE ENGLISH-DETERMINANTS-All Questions

Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0 represents a stra...
Text Solution
|
If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...
Text Solution
|
The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z ar...
Text Solution
|
Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a ...
Text Solution
|
If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...
Text Solution
|
If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, th...
Text Solution
|
Prove that |2alpha+beta+gamma+deltaalphabeta+gammadelta alpha+beta+g...
Text Solution
|
Solve for x , |[x,-6,-1], [ 2,-3x,x-3], [-3, 2x, x+2]|=0.
Text Solution
|
The value of the determinant |{:(1,,1,,1),(.^(m)C(1),,.^(m+1)C(1),...
Text Solution
|
Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a...
Text Solution
|
If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...
Text Solution
|
Consider the set A of all determinants of order 3 with entries 0 or 1 ...
Text Solution
|
Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3...
Text Solution
|
If |[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7],[x,7, 2],[ 7, 2,x]|=|[4, 5,x]...
Text Solution
|
If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...
Text Solution
|
If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...
Text Solution
|
If sum(n=1)^nalphan=a n^2+b n ,w h e r ea ,b are constants and alp...
Text Solution
|
The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z
Text Solution
|
Using properties of determinant prove that |a+b+c-c-b-c a+b+c-a-b-a a...
Text Solution
|
Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^y C(r+1)^y C(r+2)^z Cr^z C(r+1...
Text Solution
|