Question

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

Answer 1

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