Question

高数第六题怎么写

Answer 1

投影点 P(x, y, z) 在直线上，满足：
x+y-z+1 = 0 ......(1)
2x-y+z-4 = 0 .......(2)

(1)+(2): 3x - 3 = 0, x = 1
该直线在 x = 1 平面上 y-z+2=0 .........(3)
平面上取两点 A(1, -2, 0), B(1, 0, 2), 向量 AB= (0, 2, 2)

连接 P(x, y, z), M(3, -1, 2) 向量 PM (x-3, y+1, z-2)
PM 点乘 AB = 0
2(y+1) + 2 (z-2) = 0
y+z = 1 ............(4)

(3), (4) 联立解得 y = -1/2, z = 3/2

P(1, -1/2, 3/2)

Answer 2