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Show that the following points are colli...

Show that the following points are collinear :
(i) (0,7,-7), (1,4,-5), (-1, 10,-9)
(ii) (3,-5,1), (-1,0,8), (7,-10,-6)
(iii) (-2,3,5),(7,0,-1),(1,2,3)

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To show that the given points are collinear, we can use the concept of ratios. If three points A, B, and C are collinear, then the coordinates of point B can be expressed as a linear combination of the coordinates of points A and C. ### Step-by-step Solution #### Part (i): Points (0, 7, -7), (1, 4, -5), (-1, 10, -9) 1. **Let the points be defined as:** - A = (0, 7, -7) ...
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Using vector method, prove that the following points are collinear: A(6,-7,-1) B(2,-3,1) C(4,-5,0)

Using distance formula prove that the following points are collinear: A(3,-5,1), B(-1,0,8)\ a n d C(7,-10 ,-6)

Find the area of the triangle whose vertices are given below : (i) (-3,-4), (-2,-7), (-1,-9) (ii) (3,8),(-4,2), (5,1) (iii) (2,1), (3,2), (-1, 4)

Locate the following points (i) (1,-1,3) " " (ii) (-1,2,4) (iii) (-2,-4,-7) " " (iv) (-4,2,-5)

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Find the inverse of the following matrices if exist : (i) |{:(5,-3),(2,2):}| (ii) |{:(1,-3),(-1,2):}| (iii) |{:(1,0,-1),(3,4,5),(0,-6,-7):}| (iv) |{:(1,-3,3),(2,2,-4),(2,0,2):}| (v) |{:(1,2,1),(1,-1,-2),(1,2,-1):}| (vi) |{:(4,-2,-1),(1,1,-1),(-1,2,4):}|

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NAGEEN PRAKASHAN ENGLISH-INTRODUCTION OF THREE DIMENSIONAL GEOMETRY-Exercise 12 B
  1. Find the distance between the following pairs of points : (i) (-2, 1...

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  2. Show that the following points are collinear : (i) (0,7,-7), (1,4,-5...

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  3. Show that the points (0,7,10), (-1,6,6) and(-4,9,6) are the vertices o...

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  4. Show that the points (-4,-4,-1),(0,2,3) and (4,6,-3) are the vertices ...

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  5. Show that the points (-2,4,1),(-1,5,5),(2,2,5) and (1,1,1) are the ver...

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  6. Prove that the point A(1,3,0),\ B(-5,5,2),\ C(-9,-1,2)\ a n d\ D(-3,-3...

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  7. Show that the points A(1,3,4),\ B(-1,6, 10),\ C(-7,4,7)a n d\ D(-5,1,1...

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  8. Show that the points A(3,3,3,),\ B(0,6,3),\ C(1,7,7)a n d\ D(4,4,7) ar...

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  9. Show that the points A(1,2,3),\ B(-1,-2,-1),\ C(2,3,2)a n d\ D(4,7,6) ...

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  10. Show that the points A(2,-1,3),B(1,-3,1) and C(0,1,2) are the vertices...

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  11. Determine the points in i. xy-plane which re equidistant from the po...

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  12. Find a point on Z-axis which is equidistant from the points (1,5,7) an...

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  13. Find the points on z-is which are t a distance sqrt(21) from the point...

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  14. If A(-2,2,3)a n dB(13 ,-3,13) are two points. Find the locus of a poin...

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  15. If A(3,4,1) and B(-1,2,3) are two points, then find the locus of a mov...

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  16. The coordinates of the point which is equidistant from the points O(...

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  17. Find the locus of a point which moves in such a way that the sum of it...

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  18. A moving point 'P' moves such that AP^(2)+BP^(2)=10 where the co-ordin...

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