Question

show that the points( 2,3,4 ),(-1,4,5) and (8,1,2) are collinear​

Answer 1

Step-by-step explanation:

HERE IS YOUR FULL ANSWER

Answer 2

$use \: \: ab + bc = ac$

Step-by-step explanation:

$Let, \: \: a = 2i + 3j + 4k, \: b = - 1i + 4j + 5k, \: and \: \: c = 8i + 1j + 2k \\ then, \: \: ab = (- 1i + 4j + 5k) - (2i + 3j + 4k) = - 3i + 1j+ 1k \\ \: \: \: \: \: \: \: \: \: \: bc = (8i + 1j + 2k) - (- 1i + 4j + 5k) = 9 i- 3j - 3k \\ \: \: \: \: \: \: ac = (8i + 1j + 2k) - (2i + 3j + 4k) = 6 i- 2 j- 2k \\ Now, \: \: ab + bc = (- 3i + 1j+ 1k) + (9 i- 3j - 3k) \\ = 6i - 2 j- 2k = ac \\ we \: \: see \: \: that , \: \: \: \: ab + bc = ac \\ so, \: \: Hence \: \: the \: \: given \: \: points \: \: are \: \: collinear.$