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Show that the DeltaABC with vertices A (...

Show that the `DeltaABC` with vertices A ( 0,4, 1) , B ( 2, 3, -1) and C ( 4,5,0) is right angled.

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To show that triangle ABC with vertices A(0, 4, 1), B(2, 3, -1), and C(4, 5, 0) is right-angled, we will use the distance formula to calculate the lengths of the sides and then apply the Pythagorean theorem. ### Step 1: Calculate the Length of Side AB Using the distance formula: \[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \] Substituting the coordinates of points A and B: ...
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NCERT EXEMPLAR ENGLISH-INTRODUCTION TO THREE DIMENSIONAL GEOMETRY-Fillers
  1. Show that the DeltaABC with vertices A ( 0,4, 1) , B ( 2, 3, -1) and ...

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  2. The three axes OX, OY and OZ determine ………….

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  3. The three planes, determine a rectangular parallelopiped which has ………...

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  4. The coordiantes of a point are the perpendicular distance from the ….....

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  5. The Three coordiantes planes divide the space into ……. Parts.

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  6. If a point P lies in YZ- plane , then the coordinates of a point on YZ...

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  7. The equation of YZ- plane is ………

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  8. If the point P lies on Z - axis , then coordinates of p are of the for...

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  9. The equation of Z - axis , are…………..

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  10. A line is parallel to XY- plane if all the points on the line have equ...

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  11. A line is parallel to X-axis,if all the points on the line have equal…...

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  12. 45x=a represent a plane parallel to ………..

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  13. A plane is parallel to YZ-plane , so it is perpendicular tio

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  14. The length of the longest piece of a string that can be stetched strai...

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  15. If the distance between the points P(a ,2,1)a n d\ Q(1,-1,1) is 5 unit...

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  16. The coordinates of the mid points of sides AB, BC and CA of A B C are...

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  17. Match each item given under the column I to its correct answer given u...

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