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If `veca, vecb and vecc` are the position vectors of vertices A,B,C of a `Delta ABC,` show that the area of triangle ABC is `1/2| veca xx vecb + vecbxx vec c+vec c xx veca|.` Deduce the condition for points `veca, vecb and vecc` to be collinear.

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CBSE COMPLEMENTARY MATERIAL-VECTORS -FOUR MARKS QUESTIONS
  1. For any vector veca |veca xx hati|^(2) + |veca xx hatj|^(2) + |vec...

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  2. Show that (veca xx vecb)^(2) = |veca| ^(2) |vecb|^(2) - (veca.vecb)^(2...

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  3. If veca, vecb and vecc are the position vectors of vertices A,B,C of a...

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  4. Let veca , vecb , vecc be unit vectors such that veca .vecb =0=veca....

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  5. if veca + vecb + vecc=0, then show that veca xx vecb = vecb xx vecc = ...

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  6. If veca = hati + hatj + hatk, vecc = hatj - hatk are given vectors, th...

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  7. Let, veca , vecb and vecc be three non zero vectors such that vecc is ...

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  8. If the vectors vecalpha = a hati + hatj + hatk, vecbeta = hati + b hat...

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  9. Find the altitude of a parallelepiped determined by the vectors veca, ...

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  10. Prove that the four points (4hati + 5 hatj+hatk), - (hatj +hatk),(3hat...

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  11. If |veca| =3, |vecb|=4 and |vecc|=5 such that each is perpendicular to...

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  12. Decompose the vector 6 hati - 3 hatj - 6 hatk into vectors which are p...

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  13. If veca, vecb and vecc are vectors such that veca. vecb = veca.vecc, v...

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  14. If veca, vecb and vecc are three non zero vectors such that veca xx v...

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  15. For any three vectors veca, vecb, vecc the value of [(veca-vecb, vecb-...

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  16. If [veca vecbvecc]=2 find the volume of the parallelepiped whose co-te...

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  17. If veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7 , then find the ang...

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  18. If the magnitude of the vector product of the vector hati+hatj+hatk wi...

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  19. If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd show that (veca-vec...

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  20. Find a vector of magnittude sqrt(171) which is perpendicular to both o...

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