<p><strong>4. Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.</strong></p>

Given, A (2,3,4), B (-1, -2,1), C (5,8,7)Direction ratio of AB= (−1−2), (−2−3), (1−4)= (3, −5, −3)Where, a1=3, b1=-5, c1=-3Direction ratio of BC= (5− (−1)), (8− (−2)), (7−1)= (6, 10, 6)Where, a2=6, b2=10, c2=6Now, a2a1=6−3=−2b2b1=10−5=−2c2c1=6−3=−2Here, direction ratio of two-line segments are proportional.So, A, B, C are collinear.

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Ncert Solutions Maths class 12th Maths Class 12th Three Dimensional Geometry

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

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Vishal Baghel | Contributor-Level 10

4 months ago

Given,

A (2,3,4), B (-1, -2,1), C (5,8,7)

Direction ratio of AB= $\begin{array}{l} (- 1 - 2), (- 2 - 3), (1 - 4) \\ = (3, - 5, - 3) \end{array}$

Where, a₁=3, b₁=-5, c₁=-3

Direction ratio of BC= $\begin{array}{l} (5 - (- 1)), (8 - (- 2)), (7 - 1) \\ = (6, 10, 6) \end{array}$

Where, a₂=6, b₂=10, c₂=6

Now,

$\begin{array}{l} \frac{a_{2}}{a_{1}} = \frac{6}{- 3} = - 2 \\ \frac{b_{2}}{b_{1}} = \frac{10}{- 5} = - 2 \\ \frac{c_{2}}{c_{1}} = \frac{6}{- 3} = - 2 \end{array}$

Here, direction ratio of two-line segments are proportional.

So, A, B, C are collinear.

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$\vec{b} \cdot \vec{c} = - 48$ ... (2)

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

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