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If vecalpha||(vecbxxvecgamma), then (vec...

If `vecalpha||(vecbxxvecgamma), then (vecalphaxxvecbeta).(vecalphaxxvecgamma)=` (A) `|vecalpha|^2(vecbeta.vecgamma)` (B) `|vecbeta|^2(vecgamma.vecalpha)` (C) `|vecgamma|^2(vecalpha.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
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  2. If the two adjacent sides of two rectangles are reprresented by vector...

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  3. If vecalpha||(vecbxxvecgamma), then (vecalphaxxvecbeta).(vecalphaxxvec...

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  4. The position vectors of points A,B and C are hati+hatj,hati + 5hatj -h...

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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 vecr and vecs are non-zero constant vectors and the scalar b is cho...

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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, B and C of a triangle are thre...

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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 vecto veca is such tha its projections along vectors (hati ...

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

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  19. ln a quadrilateral ABCD, vec(AC) is the bisector of the (vec(AB) ^^ v...

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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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