Math, asked by rocky3041, 1 year ago

Show that points A (2,3,4) B(-1, -2, 1) and C (5, 8, 7) are colinear.

Answers

Answered by pranjaygupta
1

Step-by-step explanation:

if the determinant is zero the points are collinear

| 2 3 4|

| -1 -2 1|

| 5 8 7|

2(-14-8)-3(-7-5)+4(-8+10)

2(-22)-3(-12)+4(2)

-44+36+8

0

hence proved

hope it helps u

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Answered by Anonymous
23

\boxed{ Answer}

Solution => We have the direction ratios of AB

< -1, -2, -2,-3, 1, -4 >

i.e, < -3, -5, -3 >

or < 3, 5, 3 >

Now the direction ratios of BC are

< 5 -(-1), 8 -(-2), 7 -1 >

i.e, < 6, 10, 6 > i.e < 3, 5, 3 >

Thus

 \frac{3}{3}  =  \frac{5}{5}  =  \frac{3}{3}

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Hence AB, BC are either parallel or concident lines.

But both the lines pass through the common point B.

Hence the lines are concident and consequently the three points are collinear.

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