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If a is a nonzero real number prove that...

If a is a nonzero real number prove that the vectors
`overset(r) alpha=a hati + 2 a hatj - 3 a hatk, overset(i)beta= (2a+1) hati + (2a + 3) hatj + (a +1) hatk and overset(r) gamma = (3a + 5) overset(i) hatj + (a +2) overset(i)k` are never coplanar,

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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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