Prove that the points $A (4, - 3, - 1), B (5, - 7, 6)$ and $C (3, 1, - 8)$ are collinear.

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Solution

$- - \to A B = (5 - 4)^i + (- 7 + 3)^j + (6 + 1)^k$
$=^i - 4^j + 7^k$

$- - \to A C = (3 - 4)^i + (1 + 3)^j + (- 8 + 1)^k$
$= -^i + 4^j - 7^b$
$= - (^i - 4^j + 7^k)$

$- - \to A B = (- 1) - - \to A C$
$∴ A, B, C$ are collinear

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Similar questions

Using distance formula prove that the following points are collinear

(i) A(4, -3, -1), B(5, -7, 6) and C(3, 1, -8)

(ii) P(0,7, -7), Q(1, 4, -5) and R(-1, 10, -9)

(iii) A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)

x

A (4, 1, 2), B (5, x, 6), C (5, 1, - 1)

D (7, 4, 0)

¯ ¯¯¯¯¯¯ ¯ A C

A (- 3, - 2), B (5, - 2), C (9, 3)

D (1, 3)

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