Show that the points (2, 3, 4), (-1, -2, 1), (5, 8, 7) are collin… - Vidyadip

Question

Show that the points (2, 3, 4), (-1, -2, 1), (5, 8, 7) are collinear.

✓

Answer

Suppose the points are A(2, 3, 4), B(-1, -2, 1) and C(5, 8, 7).

We know that the direction ratios of the line joining the points (x₁, y₁, z₁) and (x₂, y₂, z₂) are x₂- x_1,y₂- y_1,z₂- z_1.

The direction ratios of AB are (-1 - 2), (-2 - 3), (1 - 4),

i.e. -3, -5, -3.

The direction ratios of BC are (5 - (-1)), (8 - (-2)), (7 - 1),

i.e. 6, 10, 6.

It can be seen that the direction ratios of BC are -2 times that of AB, i.e. they are proportional. Therefore, AB is parallel to BC.

Since point B is common in both AB and BC, points A, B, and C are collinear.

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