$xyz$座標空間に，下図のように一辺の長さ1の立方体OABC-DEFGがある．この立方体を$xy$平面上の直線$y = -x$のまわりに，頂点Fが$z$軸の正の部分にくるまで回転させる．このとき，次の問いに答えよ．
(1) 回転後の頂点Bの座標を求めよ．
(2) 回転後の頂点A，Gで定まるベクトル$\overrightarrow{\mathrm{AG}}$の成分を求めよ．
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