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if vecalpha||( vecbetaxx vecgamma) , th...

if ` vecalpha||( vecbetaxx vecgamma)` , then `( vecalphaxxbeta)dot( vecalphaxx vecgamma)` equals to `| vecalpha|^2( vecbetadot vecgamma)` b. `| vecbeta|^2( vecgammadot vecalpha)` c. `| vecgamma|^2( vecalphadot vecbeta)` d. `| vecalpha|| vecbeta|| vecgamma|`

A

`|vecalpha|^(2)(vecbeta.vecgamma)`

B

`|vecbeta|^(2)(vecgamma.vecalpha)`

C

`|vecgamma|^(2)(vecalpha.vecbeta)`

D

`|vecalpha||vecbeta||vecgamma|`

Text Solution

Verified by Experts

The correct Answer is:
a
`vecalpha|| (vecbeta xx vecgamma) Rightarrow vecalpha bot vecbeta and vecalpha bot vecgamma`
now `, ( vecalpha xx vecbeta) . (vecbeta. Vecbeta)`
`= |vecalpha| ( vecbeta. Vecgamma) - (vecalpha. Vecbeta) (vecalpha. Vecgamma)`
` |vecalpha|^(2) . (vecbeta. vecgamma)`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d|...

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  2. If the two adjacent sides of two rectangles are reprresented by vector...

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  3. if vecalpha||( vecbetaxx vecgamma) , then ( vecalphaxxbeta)dot( vecal...

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  4. The position vectors of the points P,Q,R,S are hati+hatj+hatk,2hati+5h...

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  5. Given three vectors eveca, vecb and vecc two of which are non-collinea...

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  6. If veca and vecb are unit vectors such that (veca +vecb). (2veca + 3ve...

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  7. If in a right-angled triangle A B C , the hypotenuse A B=p ,t h e n...

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  8. Resolved part of vector veca and along vector vecb " is " veca1 and th...

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  9. Let veca=2hati=hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hat...

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  10. If P is any arbitrary point on the circumcirlce of the equllateral ...

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  11. If vec ra n d vec s are non-zero constant vectors and the scalar b...

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  12. veca and vecb are two unit vectors that are mutually perpendicular. A...

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  13. Given that veca,vecb,vecp,vecq are four vectors such that veca + vecb...

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  14. The position vectors of the vertices A ,Ba n dC of a triangle are t...

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  15. If a is real constant A ,Ba n dC are variable angles and sqrt(a^2-4)ta...

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  16. The vertex A triangle A B C is on the line vec r= hat i+ hat j+lambda...

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  17. A non-zero vector vec a is such that its projections along vectors...

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  18. Position vector hat k is rotated about the origin by angle 135^0 i...

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  19. In a quadrilateral A B C D , vec A C is the bisector of vec A Ba n d ...

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  20. In fig. 2.33 AB, DE and GF are parallel to each other and AD, BG and E...

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