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            2017年成人高考專升本數學復習資料-復習指導四

            福建成人高考信息網www.laiwobuy.com 發布時間: 2017年03月27日

            四、向量代數與空間解析幾何

              (一)向量代數

              1.知識范圍

              (1)向量的概念

              向量的定義 向量的模 單位向量 向量在坐標軸上的投影 向量的坐標表示法 向量的方向余弦

              (2)向量的線性運算

              向量的加法 向量的減法 向量的數乘

              (3)向量的數量積

              二向量的夾角 二向量垂直的充分必要條件

              (4)二向量的向量積 二向量平行的充分必要條件

              2.要求

              (1)理解向量的概念,掌握向量的坐標表示法,會求單位向量、方向余弦、向量在坐標軸上的投影。

              (2)熟練掌握向量的線性運算、向量的數量積與向量積的計算方法。

              (3)熟練掌握二向量平行、垂直的充分必要條件。

              (二)平面與直線

              1.知識范圍

              (1)常見的平面方程

              點法式方程 一般式方程

              (2)兩平面的位置關系(平行、垂直和斜交)

              (3)點到平面的距離

              (4)空間直線方程

              標準式方程(又稱對稱式方程或點向式方程)一般式方程 參數式方程

              (5)兩直線的位置關系(平行、垂直)

              (6)直線與平面的位置關系(平行、垂直和直線在平面上)

              2.要求

              (1)會求平面的點法式方程、一般式方程。會判定兩平面的垂直、平行。會求兩平面間的夾角。

              (2)會求點到平面的距離。

              (3)了解直線的一般式方程,會求直線的標準式方程、參數式方程。會判定兩直線平行、垂直。

              (4)會判定直線與平面間的關系(垂直、平行、直線在平面上)。

              (三)簡單的二次曲面

              1.知識范圍

              球面 母線平行于坐標軸的柱面 旋轉拋物面 圓錐面 橢球面

              2.要求

              了解球面、母線平行于坐標軸的柱面、旋轉拋物面、圓錐面和橢球面的方程及其圖形。


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