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The edges of a parallelopiped are of uni...

The edges of a parallelopiped are of unit length and are parallel to non coplanar unit vectors `hata,hatb,hatc` such that hata.hatb=hatb.hatc=hatc.hata1/2` Then the volume of the parallelopiped is (A) `1/sqrt(2)` (B) `1/(2sqrt(2))` (C) `sqrt(3)/2` (D) 1/sqrt(3)`

A

`(1)/(sqrt2)`

B

`(1)/(2sqrt2)`

C

`(sqrt3)/(2)`

D

`(1)/(sqrt3)`

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A
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MOTION-VECTOR -EXERCISE - 4 ( LEVEL-II)
  1. Let veca, vecb ,vecc be unit vetors such that veca + vecb + vecc = ve...

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  2. Assertion: vec(PQ)xx(vec(RS)+vec(ST))!=0, Reason : vec(PQ)xxvec(RS)=ve...

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

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  4. Lelt two non collinear unit vectors hata and hatb form and acute angle...

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  5. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(ve...

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  6. Let P, Q, R and S be the points on the plane with position vectors -2h...

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  7. If veca and vecb are vectors in space given by veca=(hati-23hatj)/(sqr...

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  8. Let veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj...

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  9. The vectors which is/are coplanar with vectors hati+hatj+2hatk and hat...

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  10. Let veca=-hati-hatk, vecb=-hati+hatj and vecc=hati+2hatj+3hatk be th...

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  11. Let bar(PR)=3hati+hatj-2hatk and bar(SQ)=hati-3hatj-4hatk determine d...

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  12. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

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  13. Let vecx,vecy and vecz be three vector each of magnitude sqrt(2) an...

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  14. Let veca, vecb and vecc be non - coplanar unit vectors, equally inclin...

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  15. Let triangle PQR be a triangle. Let veca = vec(QR) , vecb = vec(RP) a...

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  16. Let vecu = u(1)hati + u(2)hatj +u(3)hatk be a unit vector in R^(3) a...

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  17. Let O be the origin and let PQR be an arbitrary triangle. The point S ...

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  18. Let O be the origin and OX, OY, OZ be three unit vectors in the direct...

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  19. Let O be the origin and vec(OX) , vec(OY) , vec(OZ) be three unit vec...

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  20. Letveca and vecb be two unit vectors such that veca.vecb=0. For some x...

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