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Let (veca (x) = (sin x) hati+ (cos x) ha...

Let `(veca (x) = (sin x) hati+ (cos x) hatj and vecb(x) = (cos 2x) hati + (sin 2x) hatj` be two variable vectors `( x in R)`. Then `veca (x) and vecb (x) ` are

A

collinear for unique value of x

B

perpendicular for infinte values of x.

C

zero vectors for unique value of x

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
if `veca ( x) and vecb are bot, "then" veca. Vecb =0`
`Rightarrow sin x cos 2x + cos x sin 2x =0`
`sin (3x) =0 = sin 0 `
` 3x = npi 0or x = (npi)/3`
therefore, the two vectors are `bot` for infinite values.
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If veca=2hati + hatj + hatk,vecb=hati + 2hatj + 2hatk ,vecc= hati + ha...

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  2. If veca=2hati + hatj+ hatk, vecb= hati+ 2hatj + 2hatk,vecc = hati+ hat...

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

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

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

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

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

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

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  9. If V be the volume of a tetrahedron and V ' be the volume of anothe...

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  10. [(veca xxvecb)xx(vecb xx vecc) (vecb xxvecc) xx (vecc xxveca) (veccxxv...

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

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  12. If the vectors veca and vecb are perpendicular to each other then a ve...

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  13. If veca,' = hati + hatj, vecb'= hati - hatj + 2hatk nad vecc' = 2hati ...

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

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  15. If the unit vectors veca and vecb are inclined of an angle 2 theta ...

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  16. vecb and vecc are non- collinear if veca xx (vecb xx vecc) + (veca .ve...

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  17. Let veca.vecb=0 where veca and vecb are unit vectors and the vector ve...

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  18. veca and vecb are two given vectors. On these vectors as adjacent side...

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  19. If vecca xx (vec b xx vecc) is perpendicular to (veca xx vecb ) xx vec...

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  20. If vecp=(vecbxxvecc)/([(veca,vecb,vecc)]),vecq=(veccxxveca)/([(veca,ve...

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