立體直角坐標系內(nèi)平面的特征經(jīng)典練習題

立體直角坐標系內(nèi)平面的特征經(jīng)典練習題一、選擇題（每題1分，共10分）1.平面x+y+z=1與坐標軸z的交點為：a)(1,0,0)b)(0,1,0)c)(0,0,1)d)(1,1,0)2.平面2x-y-3z=4與坐標軸x的交點為：a)(2,0,0)b)(0,-4,0)c)(-2,0,0)d)(0,0,4)3.平面x+y=0與坐標軸z的交點為：a)(0,0,1)b)(1,-1,0)c)(0,1,0)d)(0,0,0)4.平面2x-y+z=0與坐標軸y的交點為：a)(-3,0,6)b)(0,0,0)c)(0,3,0)d)(0,0,-6)5.平面2x-y+z=2與坐標軸x的交點為：a)(-1,0,0)b)(2,0,0)c)(0,0,-2)d)(0,2,0)6.平面x+y+z=0與坐標軸y的交點為：a)(0,0,0)b)(-1,1,0)c)(1,-1,0)d)(0,-1,0)7.平面2x-y+3z=6與坐標軸z的交點為：a)(0,-3,2)b)(2,0,0)c)(0,-6,0)d)(-3,0,2)8.平面x+y-3z=4與坐標軸y的交點為：a)(-4,0,2)b)(4,0,-2)c)(0,0,0)d)(0,4,-2)9.平面x+y+z=-2與坐標軸z的交點為：a)(-2,0,2)b)(0,-2,2)c)(-2,0,0)d)(2,-2,0)10.平面-3x+y+z=0與坐標軸x的交點為：a)(0,0,0)b)(-1,0,3)c)(1,3,0)d)(-1,3,0)二、填空題（每題2分，共20分）1.平面\(2x-y+z=5\)與坐標軸\(x\)軸、\(y\)軸、\(z\)軸的交點分別為\(\_\_\_\_\_\_\_\)。2.平面\(x-y-z=0\)與坐標軸\(x\)軸、\(y\)軸、\(z\)軸的交點分別為\(\_\_\_\_\_\_\_\)。3.平面\(x+y=0\)與坐標軸\(x\)軸、\(y\)軸、\(z\)軸的交點分別為\(\_\_\_\_\_\_\_\)。4.平面\(2x-y+z=1\)與坐標軸\(x\)軸、\(y\)軸、\(z\)軸的交點分別為\(\_\_\_\_\_\_\_\)。5.平面\(2x-y+z=3\)與坐標軸\(x\)軸、\(y\)軸、\(z\)軸的交點分別為\(\_\_\_\_\_\_\_\)。三、解答題（每題10分，共20分）1.平面\(x+2y+z=4\)與坐標軸\(x\)軸、\(y\)軸、\(z\)軸的交點分別為多少個？請列出所有交點的坐標。2.設(shè)平面\(\alpha\)與平面\(\beta\)的方程分別為\(2x+3y-z=0\)和\(3x-4y-5z=0\)，求平面\(\alpha\)和平面\(\beta\)的交線方程。四、應用題（每題15分，共30分）1.已知平面\(\alpha\)與坐標軸的交點為\(A(1,0,0)\)，\(B(0,1,0)\)，\(C(0,0,-1)\)，求平面\(\alpha\)的方程。2.平面\(\alpha\)經(jīng)過點\(A(2,1,0)\)，平面\(\beta\)經(jīng)過點\(B(2,0,1)\)，求平面\(\