Home
Class 12
MATHS
If x,y, z are in A.P., then the values o...

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

A

1

B

0

C

2a

D

a

Text Solution

Verified by Experts

The correct Answer is:
B
since x,y,z are in A.P. therefore `x+z-2y=0` Now
`|{:(a+2,,a+3,,a+2x),(a+3,,a+4,,a+2y),(a+4,,a+5,,a+2x):}|=|{:(0,,0,,2(x+z-2y)),(a+3,,a+4,,a+2y),(a+4,,a+5,,a+2z):}|`
Applying `R_(1) to R_(1) +R_(3) -2R_(2)`
`=|{:(0,,0,,0),(a+3,,a+4,,a+2y),(a+4,,a+5,,a+2z):}|" "[ :' x +z -2y =0]`
`=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

If x , y , z are in A.P. , then the value of the determinant are in A.P. , then the value of the determinant |a+2a+3a+2x a+3a+4a+2y a+4a+5a+2z| is a. 1 b. 0 c. 2a d. a

If x = 1, y = 2, z = 5 , then find the value of 3x – 2y + 4z.

If x = 2a- 1, y = (2a - 2) and z =3 - 4a, then the value of x ^(3) + y ^(3) + z ^(3) will be :

If x : y : z = 3 : 4 : 9, then what will be the value of (2x + 3y + z) : (2z + x – 3y)?

3x - [4y - {7x - (3z - 2y) + 4z - 3(x + 3y - 2z)}]