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Show that vectors ` vec a ,\ vec b ,\ vec c` are coplanar if ` vec a+ vec b ,\ vec b+ vec c ,\ vec c+ vec a` are coplanar.

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To show that the vectors \( \vec{a}, \vec{b}, \vec{c} \) are coplanar if the vectors \( \vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a} \) are coplanar, we can use the property of the scalar triple product. ### Step-by-Step Solution: 1. **Understanding Coplanarity**: Vectors \( \vec{u}, \vec{v}, \vec{w} \) are coplanar if the scalar triple product \( \vec{u} \cdot (\vec{v} \times \vec{w}) = 0 \). 2. **Expressing the Given Vectors**: ...
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RD SHARMA-SCALAR TRIPLE PRODUCT -Solved Examples And Exercises
  1. The four points whose position vector are 6 hat i - 7 hat j,16 hat i -...

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  2. For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ vec b...

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  3. Show that vectors vec a ,\ vec b ,\ vec c are coplanar if vec a+ v...

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  4. Show that the vectors vec a - vec b, vec b - vec c , vec c - vec a are...

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  5. Evaluate the following: [ hat i\ hat j\ hat k]+[ hat j\ hat k\ ...

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  6. Evaluate : [ hat i hat j hat k]+[ hat j hat k hat i]+[ hat k hat i...

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  7. Find [ vec a\ vec b\ vec c] , when : vec a=2 hat i-3 hat j ,\ vec ...

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  8. Find [ vec a\ vec b\ vec c] , when : vec a= hat i-2 hat j+3 hat k ,...

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  9. Find the volume of the parallelepiped whose coterminous edges are re...

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  10. Find the volume of the parallelepiped whose coterminous edges are r...

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  11. Find the volume of the parallelepiped whose coterminous edges are r...

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  12. Find the volume of the parallelepiped whose coterminous edges are r...

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  13. Show that each of the following triads of vectors are coplanar: vec...

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  14. Show that each of the following triads of vectors are coplanar: vec...

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  15. Show that each of the following triads of vectors are coplanar: ve...

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  16. Find the value of lambda so that the following vectorts are coplana...

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  17. Find the value of lambda so that the following vectorts are coplana...

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  18. Find the value of lambda so that the following vectorts are coplana...

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  19. Find the value of lambda so that the following vectorts are coplanar...

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  20. Show that the points having position vectors 6 hat i-7 hat j ,\ 16 ...

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