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If veca=2hati + 3hatj+ 8hatk is perpendi...

If `veca=2hati + 3hatj+ 8hatk` is perpendicular to `vecb= 4hati-4hatj + alphahatk`, then find the value of `alpha`

A

`-1/2`

B

`1/2`

C

1

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
a
` veca xx (vecb xx vecc) = (veca .vecc) vecb -(veca.vecb) vecc`
` = 5 (hati + 2hatj + 2hatk) - 6 (hati + hatj + 2hatk) `
`Rightarrow ( 1 + alpha) hati + beta (1 + alpha) hatj + gamma ( 1+ alpha) (1+beta) hatk`
` = - hati + 4hatj - 2hatk`
` Rightarrow 1 + alpha = -1 , beta = -4 and gamma (n -1) (-3) = (-2)`
` Rightarrow gamma = -2/3`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  2. If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2h...

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  3. If veca=2hati + 3hatj+ 8hatk is perpendicular to vecb= 4hati-4hatj + a...

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  4. Let veca (x) = (sin x) hati+ (cos x) hatj and vecb(x) = (cos 2x) hati ...

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  5. For any vectors veca and vecb, (veca xx hati) . (vecb xx hati) + ( vec...

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  6. If veca,vecb and vecc are three non coplanar vectors and vecr is any v...

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  7. If vecP = (vecbxxvecc)/([vecavecbvecc]).vecq=(veccxxveca)/([veca vecb ...

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  8. A(veca),B(vecb),C(vecc) are the vertices of the triangle ABC and R(vec...

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  9. If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is ...

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  11. [( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)(...

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  12. If vecr=x(1)(vecaxx vecb) + x(2) (vecb xxvecc) + x(3)(vecc xxveca) and...

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  13. If veca bot vecb then vector vecv in terms of veca and vecb satisfying...

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  14. If vec a^'= hat i+ hat j , vec b^' hat i- hat j+2 hat ka n d vec c^'2...

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  15. If veca= hati +hatj, vecb= hatj + hatk, vecc = hatk + hati then in th...

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  17. vec a, vec ba n d vec c are non-collinear if vec axx( vec bxx vec c)+...

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  18. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

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  19. If vectors vec aa n d vec b are two adjacent sides of a parallelogr...

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