Vector Cross Product and Trigonometric Inequality

Between the following two statements :
Statement-I : Let

→

a

=

^

i

+2

^

j

−3

^

k

‌‌ and

→

b

=2

^

i

+

^

j

−

^

k

. Then the vector

→

r

satisfying

→

a

×

→

r

=

→

a

×

→

b

and

→

a

⋅

→

r

=0 is of magnitude √10.
Statement-II : In a triangle ABC,cos‌2‌A+cos‌2‌B
+cos‌2‌C≥−‌

3

2

.