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Question

x, y, z are in AP with common difference d.

∣ ∣x+yy1y+zz1z+xx1∣ ∣ =



Your Answer
A
2 d2
Correct Answer
B
-3d2
Your Answer
C
- d2
Your Answer
D
d

Solution

The correct option is B -3d2

You can use the property of the determinant that if the terms of one row is given as a sum of two other terms then the determinant can be written as the sum of two determinants as given below,

∣ ∣x+yy1y+zz1z+xx1∣ ∣ = ∣ ∣xy1yz1zx1∣ ∣ + ∣ ∣yy1zz1xx1∣ ∣

∣ ∣xy1yz1zx1∣ ∣ + 0

R2R2R1
R3R3R1

= ∣ ∣xy1yxzy0zxxy0∣ ∣

= ∣ ∣xy1dd02dd0∣ ∣

= + 1(d22d2)
= - 3d2

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