Show that the points $(2, - 1, 3), (4, 3, 1)$ and $(3, 1, 2)$ are collinear.

Open in App

Solution

$X_{1}, Y_{1}, Z_{1}$ = $2, - 1, 3$
$X_{2}, Y_{2}, Z_{2}$ = $4, 3, 1$
$X_{3}, Y_{3}, Z_{3}$ = $3, 1, 2$

$\frac{X_{1} - X_{2}}{X_{2} - X_{3}} = \frac{Y_{1} - Y_{2}}{Y_{2} - Y_{3}} = \frac{Z_{1} - Z_{2}}{Z_{2} - Z_{3}}$

$\frac{- 2}{1} = \frac{- 4}{2} = \frac{2}{- 1}$

$\frac{- 2}{1} = \frac{- 2}{1} = \frac{- 2}{1}$
Hence, the points are coplanar.

Suggest Corrections

Similar questions

Show that the points (1, – 1), (5, 2) and (9, 5) are collinear. [2 MARKS]

P (2, 4, 6), Q (- 2, - 2, - 2)

R (6, 10, 14)

(2, 3), (3, 1)

(1, 5)

(5, 4, 2), (6, 2, - 1)

(8, - 2, - 7)

Join BYJU'S Learning Program