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The number of distinct real values of la...

The number of distinct real values of `lamda,` for which the vectors :
`-lamda ^(2) hati+hatj+ hatk, hati - lamda ^(2) hatj+ hatk and hati + hatj- lamda ^(2) hatk` are coplanar, is :

A

zero

B

one

C

two

D

three.

Text Solution

Verified by Experts

The correct Answer is:
C
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The vectors lamda hati + hatj + 2 hatk, hati + lamda hatj - hatk and 2 hati - hatj + lamda hatk are coplanar if :

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Value of a for which 2 hati - hatj+1hatk , hati + 2 hatj - 3 hatk and 3 hati + a hatj + 5 hatk are coplanar is :

The valur of 'lamda' for which the two vectors : 2 hati - ahtj + 2 hatk and 3 hati + lamda hatj + ahtk are perpendicular is :

The value of 'lamda' which the vectors : 3 hati - 6 hatj + hatk and 2 hati - 4 hatj + lamda hatk are parallel is :

The three vectors 7 hati - 11 hatj + hatk, 5 hati + 3 hatj - 2 hatk, 12 hati - 8 hatj- hatk from :

The vector veca = hati + hatj + (m + 1) hatk , vecb = hati + hatj + m hatk.vecc = hati - hatj + m hatk are coplanar for :

The vectors 2 hati - ahtj + hatk, hati -3 hatj - 5 hatj and sqrt3 hati - 4 hatj - 4 hatk are the sides of a triange, which is :

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MODERN PUBLICATION-VECTOR ALGEBRA -Multiple Choice Question (Level-II)
  1. Let vecu = hati+ hatj, vecv = hati - hatj and vecw= hati + 2 hatj + 3 ...

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  2. Let veca, vecb and vecc be three non-zero vectors such that no two of ...

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  3. Let veca, vecb, and vecc be three non-zero vectors such that no two of...

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  4. If veca = (hati +hat j + hatk), veca.vecb=1 and veca xx vecb=hatj-hatk...

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  5. If veca, vecb, cecc are non-coplanar vectors and lamda is a real numbe...

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  6. If hatu and hatv are unit vactors and theta is the angle between them,...

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  7. Let veca = hat i + hatj + hatk, vecb = hati + 2 hatk and vecc = x hati...

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  8. The vector veca = alpha hati + 2 hatj + beta hatk lies in the plance o...

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  9. The non-zero vectors veca, vecb and vecc are related by veca = 8 vecb ...

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  10. Let the vectors veca, vecb, vecc and vecd be such that (veca xx vecb) ...

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  11. The unit vector which is orthgonal to the vector veca=3hati+2hatj+6hat...

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  12. If veca, vecb, vecc are three non-zero, non-coplanar vectors and vec...

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  13. Let veca = hati + hatj + hatk, vecb = hati - ahtj + hatk and hati - ha...

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  14. The number of distinct real values of lamda, for which the vectors : ...

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  15. Let veca, vecb, vecc be unit vectors such that veca + vecb + vecc = v...

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  16. The edges of a parallelopiped are of unit length and are parallel to n...

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  17. Let two non-collinear unit vectors hata and hatb form an acute angle. ...

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  18. If vec u , vec nu, and vec w are non coplanar vectors and p,q are real...

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  19. If veca , vecb, vecc and vecd are unit vectors such that (veca xx vecb...

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  20. Let (P (3,2,6) be a point in space and Q be point on the line vecr = (...

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