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If veca , vec b , vec c are unit vecto...

If ` veca , vec b , vec c` are unit vectors such that ` veca+ vec b+ vecc= vec0`find the value of ` veca cdot vec b+ vecb cdot vecc+ vecc cdot veca`.

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Verified by Experts

Given, `veca+ vecb+ vecc=0`
Squaring both the sides,
`|veca + vecb + vecc|^2 = 0` ...
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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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