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If in triangle ABC, vec(AB) = vecu/|vec...

If in triangle ABC, ` vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (2vecu)/|vecu| , " where " |vecu| ne |vecv|` , then

A

`1 + cos 2A + cos 2B + cos 2C=0`

B

`sin A = cos C`

C

projection of AC on BC is equal to BC

D

projection of AB on BC is equal to AB

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The correct Answer is:
a,b,c
` vec(AB) + vec(BC) = vec(AC)`
`vec(BC) = (2vecu)/|vecu|- vecu/|vecu|+vecv/|vecv|= vecu/|vecu|+ vecv/|vecv|`
` vec(AB). vec(BC) = (vecu/|vecu|- vecv/|vecv|)(vecu/|vecu|+vecv/|vecv|)`
`(hatu - hatv . (hatu +hatv) = 1-1 =0`
v
`Rightarrow 1+ cos 2A + cos2B+ cos2C=0`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Let veca, vecb, and vecc be three non- coplanar vectors and vecd be a ...

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  2. If veca, vecb and vecc are three unit vectors such that veca xx (vecb ...

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  3. If in triangle ABC, vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (...

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  4. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

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  5. The scalars l and m such that lveca + m vecb =vecc, " where " veca, ve...

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  6. If (veca xxv vecb) xx (vecc xx vecd) . (veca xx vecd) =0 then which of...

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  7. A,B C and dD are four points such that vec (AB) = m(2 hati - 6 hatj +...

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  8. If the vectors veca, vecb, vecc are non -coplanar and l,m,n are distin...

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  9. Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(...

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  10. If vectors vecA=2hati+3hatj+4hatk, vecB=hati+hatj+5hatk and vecC form ...

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  11. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc= ...

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  12. If veca xx (vecbxx vecc)= (veca xx vecb)xxvecc then

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  13. A vector vecd is equally inclined to three vectors veca=hati-hatj+hatk...

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  14. A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, ...

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  15. <b>Statement 1:</b> Vector vecc = -5hati + 7 hatj + 2hatk is along th...

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  16. Statement1: A component of vector vecb = 4hati + 2hatj + 3hatk in the ...

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  17. Statement 1: Distance of point D( 1,0,-1) from the plane of points A( ...

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  18. Let vecr be a non - zero vector satisfying vecr.veca = vecr.vecb =vecr...

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  19. Statement 1: If a(1)hati + a(2)hatj + a(3)hatk, vecb(1)hati+b(2)hatj +...

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  20. Statement 1: vecA=2hati + 3hatj + 6hatk , vecB=hati + hatj - 2hatk and...

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