已知a=(2,-1,3),b=(-1,4,-2),c=(7,5,x),若a,b,c三向量共面,则实数x等于
问题描述：
已知a=(2,-1,3),b=(-1,4,-2),c=(7,5,x),若a,b,c三向量共面,则实数x等于
答
65/7
答
c = k1a + k2b
(7,5,x) = (2k1-k2, -k1+4k2, 3k1-2k2)
=>
7 = 2k1-k2 (1) and
5= -k1+4k2 (2) and
x = 3k1-2k2 (3)
(1) + 2(2)
7k2= 17, => k2 = 17/7
k1 = 16/7
from (3)
x = 3(16/7) - 2(17/7)
= 2