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Question

What is the value of determinant given if x, y, z are in AP with common difference d.

∣∣ ∣∣x+yy1y+zz1z+xx1∣∣ ∣∣


A

2d2

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B

d2

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C

3d2

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D

d2

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Solution

The correct option is C

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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