Question

if the point A(3,-2,4),B(1,1,1) and C(-1,4,-2) are collinear then (c:AB)=__

Answer 1

Answer:

i cant understanf this is imperfect question becausw cordinate : length cannot be found. correct tje qiestion

Answer 2

The ratio of AC : BC is 2 : 1.

Step-by-step explanation:

The points A(3,-2, 4), B(1, 1, 1) and C(-1, 4,-2) are collinear.

To find, AC : AB = ?

Using distance formula,

$\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1})^2}$

$AB=</strong>\sqrt{(1-3)^2+(1+2)^2+(1-4)^2}$

$=\sqrt{(-2)^2+(3)^2+(-3)^2}$

$=\sqrt{4+9+9}=\sqrt{22}$

$AC=\sqrt{(-1-3)^2+(4+2)^2+(-2-4)^2}$

$=\sqrt{(-4)^2+(6)^2+(-6)^2}$

$=\sqrt{16+36+36}=\sqrt{88}$

$=\sqrt{4\times 22}$

$=2\sqrt{22}$

∴ AC : AB $=2\sqrt{22}:\sqrt{22}$

= 2 : 1

Hence, the ratio of AC : BC is 2 : 1.