Motivated by [J. Algebraic Geom. 27 (2018), pp. 203–209] and [C. R. Math. Acad. Sci. Paris 354 (2016), pp. 936–939], we show the equality
(
[
X
]
−
[
Y
]
)
⋅
[
A
1
]
=
0
\left ( [ X ] - [ Y ] \right ) \cdot [ \mathbb {A} ^{ 1 } ] = 0
in the Grothendieck ring of varieties, where
(
X
,
Y
)
( X, Y )
is a pair of Calabi-Yau 3-folds cut out from the pair of Grassmannians of type
G
2
G _{ 2 }
.