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Show that the points A(1, 2, 7), B(2, 6...

Show that the points A(1, 2, 7), B(2, 6, 3) and `C(3, 10 , 1)`are collinear.

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To show that the points A(1, 2, 7), B(2, 6, 3), and C(3, 10, 1) are collinear, we will find the vectors AB and AC and check if they are scalar multiples of each other. ### Step 1: Find the vector AB The vector AB can be calculated using the coordinates of points A and B. \[ \text{AB} = B - A = (2 - 1, 6 - 2, 3 - 7) = (1, 4, -4) \] ...
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NCERT-VECTOR ALGEBRA-EXERCISE 10.3
  1. Find the angle between two vectors vecaand vecbwith magnitudes sqrt...

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  2. Find the projection of the vector hat i- hat jon the vector hat i+ ...

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  3. Find the angle between the vectors hat i-2 hat j+3kand 3 hat i-2 hat...

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  4. Show that each of the given three vectors is a unit vector: 1/7(2 hat...

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  5. Find the projection of the vector hat i+3 hat j+7 hat kon the vector...

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  6. Evaluate the product (3 veca-5 vecb)cdot(2 veca+7 vecb)

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  7. Find | vec a|and | vec b|, if ( vec a+ vec b)dot(( vec a- vec b))=8a...

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  8. Find | vecx|, if for a unit vector veca ,( vec x- veca) .( vecx+ ve...

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  9. Find the magnitude of two vectors vec aand vecbhaving the same magn...

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  10. If veca cdot veca=0and veca cdot vecb=0, then what can be conclude...

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  11. If veca , vec b , vec c are unit vectors such that veca+ vec b+ vec...

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  12. If veca=2 hat i+2 hat j+3 hat k , vecb=- hat i+2 hat j+ hat k and v...

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  13. Show that | veca| vecb+| vecb| veca is perpendicular to | vec a| vec ...

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  14. Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10 , 1)are colli...

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  15. Show that the vectors 2 hat i- hat j+ hat k , hat i-3 hat j-5 hat kan...

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  16. If either veca= vec0or vecb= vec0, then veca * vecb = 0 But the con...

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  17. If the vertices A, B, C of a triangle ABC are (1, 2, 3), (1, 0, 0), (...

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  18. If vec ais a nonzero vector of magnitude a and lambdaa nonzero scal...

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