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A vector of magnitude 10 along the no...

A vector of magnitude 10 along the normal to the curve `3x^2+8x y+2y^2-3=0` at its point `P(1,0)` can be `6 hat i+8 hat j` b. `-8 hat i+3 hat j` c. `6 hat i-8 hat j` d. `8 hat i+6 hat j`

A

`6hati + 8hatj`

B

`-8 hati + 3hatj`

C

`6hati - 8 hatj`

D

`8 hati + 6 hatj`

Text Solution

Verified by Experts

The correct Answer is:
a
Differentiate the curve
`6x + 8 ( xy_(1) + y) + 4 yy_(1) =0`
`m_(T)at (1,0) is 6 + 8 (y_(1)(0)) =0`
` y_(1) (0) = -3/4`
`m_(N)= 4/3`
Unit vector =` +- (3hati + 4hatj) / 5`
Again normal of magnitude ` 10 =+- (6hati + 8hatj)`
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A vector of magnitude 10 along the normal to the curve 3x^(2)+8xy+2y^(2)-3=0 at its point P(1,0) can be (A) 6hat i+8hat j(B)-8hat i+3hat j(C)6hat i-8hat j(D)8hat i+6hat j

If vectors vec A=2 hat i+3 hat j+4 hat k , vec B= hat i+ hat j+5 hat ka n d vec C form a left-handed system, then vec C is a. 11 hat i-6 hat j- hat k b. -11 hat i+6 hat j+ hat k c. 11 hat i-6 hat j+ hat k d. -11 hat i+6 hat j- hat k

If 4 hat i+7 hat j+8 hat k ,2 hat i+3 hat j+24a n d2 hat i+5 hat j+7 hat k are the position vectors of the vertices A ,Ba n dC , respectively, of triangle A B C , then the position vecrtor of the point where the bisector of angle A meets B C is a. 2/3(-6 hat i-8 hat j- hat k) b. 2/3(6 hat i+8 hat j+6 hat k) c. 1/3(6 hat i+13 hat j+18 hat k) d. 1/3(5 hat j+12 hat k)

Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k be three vectors. A vector in the plane of vec ba n d vec c , whose projection on vec a is of magnitude sqrt(2//3) , is a. 2 hat i+3 hat j-3 hat k b. 2 hat i-3 hat j+3 hat k c. -2 hat i- hat j+5 hat k d. 2 hat i+ hat j+5 hat k

Vectors vec A=hat i+hat j-2hat k and vec B=3hat i+3hat j-6hat k are

Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i- hat j- hat k be three vectors. A vector vec v in the plane of vec aa n d vec b , whose projection on vec c is 1/(sqrt(3)) is given by a. hat i-3 hat j+3 hat k b. -3 hat i-3 hat j+3 hat k c. 3 hat i- hat j+3 hat k d. hat i+3 hat j-3 hat k

Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i+ hat j- hat kdot A vector in the plane of vec a and vec b whose projection of c is 1//sqrt(3) is a. 4 hat i- hat j+4 hat k b. 3 hat i+ hat j+3 hat k c. 2 hat i+ hat j+2 hat k d. 4 hat i+ hat j-4 hat k

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i-3 hat k) are collinear.

Vectors vec a=-4 hat i+3 hat k ; vec b=14 hat i+2 hat j-5 hat k are laid off from one point. Vector hat d , which is being laid of from the same point dividing the angle between vectors vec aa n d vec b in equal halves and having the magnitude sqrt(6), is a. hat i+ hat j+2 hat k b. hat i- hat j+2 hat k c. hat i+ hat j-2 hat k d. 2 hat i- hat j-2 hat k

The vector vec b=3 hat i+4 hat k is to be written as the sum of a vector vecalpha parallel to vec a= hat i+ hat j and a vector vecbeta perpendicular to vec adot Then vecalpha= 3/2( hat i+ hat j) b. 2/3( hat i+ hat j) c. 1/2( hat i+ hat j) d. 1/3( hat i+ hat j)

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If (vecaxxvecb)xx(vecbxxvecc)=vecb, where veca,vecb and vecc are non z...

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  2. If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and...

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  3. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y...

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  4. If veca and vecb are two unit vectors inclined at an angle pi//3 then ...

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  5. If veca and vecb are othogonal unit vectors, then for a vector vecr no...

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  6. If veca+vecb ,vecc are any three non- coplanar vectors then the equa...

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  7. Sholve the simultasneous vector equations for vecx aedn vecy: vecx+vec...

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  8. The condition for equations vecrxxveca = vecb and vecr xx vecc = vecd ...

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

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

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

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

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

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

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

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

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

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

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

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

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