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For any three vectors veca, vecb, vecc t...

For any three vectors `veca, vecb, vecc` the value of `[(veca-vecb, vecb-vecc, vecc-veca)]`, is

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For any these vectors veca,vecb, vecc the expression (veca-vecb).{(vecb-vecc)xx(vecc-veca)} equals

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) = 2 veca.vecb xx vecc .

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of (vecaxxveca\')+(vecbxxvecb)+(vecccxxveccc\') is (A) veca+vecb+vec (B) veca\'+vecb\'+vec\' (C) 0 (D) none of these

For any three vectors veca, vecb and vecc write value of the following veca xx (vecb + vecc) + vecb xx (vecc + veca)+ vecc xx (veca + vecb)

If veca,vecbandvecc are unit vectors such that veca+vecb+vecc=0 , then the value of veca.vecb+vecb.vecc+vecc.veca is

For three vectors veca, vecb and vecc , If |veca|=2, |vecb|=1, vecaxxvecb=vecc and vecbxxvecc=veca , then the value of [(veca+vecb,vecb+vecc,vecc+veca)] is equal to

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of [veca\' vecb\' vecc\']^-1 is (A) 2[veca vecb vecc] (B) [veca,vecb,vecc] (C) 3[veca vecb vecc] (D) 0

Statement 1: If V is the volume of a parallelopiped having three coterminous edges as veca, vecb , and vecc , then the volume of the parallelopiped having three coterminous edges as vec(alpha)=(veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc vec(beta)=(veca.vecb)veca+(vecb.vecb)vecb+(vecb.vecc)vecc vec(gamma)=(veca.vecc)veca+(vecb.vecc)vecb+(vecc.vecc)vecc is V^(3) Statement 2: For any three vectors veca, vecb, vecc |(veca.veca, veca.vecb, veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|=[(veca,vecb, vecc)]^(3)

If veca, vecb and vecc are three non - zero and non - coplanar vectors such that [(veca,vecb,vecc)]=4 , then the value of (veca+3vecb-vecc).((veca-vecb)xx(veca-2vecb-3vecc)) equal to

If veca,vecb,vecc are three unit vectors such that veca+vecb+vecc=0, then veca.vecb+vecb.vecc+vecc.veca is equal to (A) -1 (B) 3 (C) 0 (D) -3/2

CBSE COMPLEMENTARY MATERIAL-VECTORS -FOUR MARKS QUESTIONS
  1. Prove that the four points (4hati + 5 hatj+hatk), - (hatj +hatk),(3hat...

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

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

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

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

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

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

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

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

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

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

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  12. If a is a nonzero real number prove that the vectors overset(r) alph...

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  13. If with reference to a right handed system of mutually perpendicula...

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  14. Find a unit vector perpendicular to plane ABC when position vectors of...

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  15. Find a unit vector in XY plane which makes an angle 45^(@) with the ve...

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  16. Suppose veca = lamda hati - 7 hatj + 3 hatk, vecb = lamda hati + hatj ...

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  17. Let vecV = 2hati +hatj - hatk and vecW= hati + 3hatk . if vecU is a u...

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  18. Let veca=hati-hatk, vecb=xhati+hatj+(1-x)hatk and vecc=yhati+xhatj+(1+...

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  19. Let a, b and c be distinct non-negative numbers. If vectos a hati +a h...

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  20. If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3)|=0 and the vectors A-=(1...

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