Let \( \mathbf{a}, \mathbf{b} \) and \( \mathbf{c} \) be three non-coplanar vectors and \( \math...

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Let \( \mathbf{a}, \mathbf{b} \) and \( \mathbf{c} \) be three non-coplanar vectors and \( \mathbf{d} \) be \( \mathbf{a} \) non-zero vector, which is perpendicular to \( a+b+c \) Now, if \( d=(\sin x)(a \times b)+(\cos y)(b \times c)+2(c \times a) \), then minimum value of \( x^{2}+y^{2} \) is equal to
(a) \( \pi^{2} \)
(b) \( \frac{\pi^{2}}{2} \)
(c) \( \frac{\pi^{2}}{4} \)
(d) \( \frac{5 \pi^{2}}{4} \)
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