Home
Class 11
MATHS
Resolved part of vector veca and along v...

Resolved part of vector `veca` and along vector `vecb " is " veca1` and that prependicular to `vecb " is " veca2` then `veca1 xx veca2` is equl to

A

`((vecaxxvecb).vecb)/(|vecb|^(2))`

B

`((veca.vecb)veca)/(|veca|^(2))`

C

`((veca.vecb)(vecbxxveca))/(|vecb|^(2))`

D

`((veca.vecb)(vecbxxveca))/(|vecbxxveca|)`

Text Solution

Verified by Experts

The correct Answer is:
c
`veca_(1) = (veca.hatb) hatb = (( veca.vecb)vecb)/(|vecb|^(2))`
` Rightarrow veca_(2) = veca -veca_(1) = veca - ((veca. Vecb)vecb)/(|vecb|^(2))`
Thus ` veca_(1) xx veca_(2) = ((veca.vecb)vecb)/(|vecb|^(2) xx )(veca - ((veca.vecb)vecb)/(|vecb|^(2)))`
` ((veca. vecb)(vecb xx veca))/(|vecb|^(2))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Single Question)|28 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Multiple Question)|11 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.3|18 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1316 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|320 Videos

Similar Questions

Explore conceptually related problems

The resolved part of the vector veca along the vector vecb is veclamda and that perpendicular to vecb is vecmu . Then (A) veclamda=((veca.vecb).veca)/veca^2 (B) veclamda=((veca.vecb).vecb)/vecb^2 (C) vecmu=((vecb.vecb0veca-(veca.vecb)vecb)/vecb^2 (D) vecmu=(vecbxx(vecaxxvecb))/vecb^2

If veca and vecb are two vectors, such that |veca xx vecb|=2 , then find the value of [veca vecb veca xx vecb]

Knowledge Check

  • If the vectors veca and vecb are mutually perpendicular, then veca xx {veca xx {veca xx {veca xx vecb}} is equal to:

    A
    `|veca|^(2)vecb`
    B
    `|veca|^(3)vecb`
    C
    `|veca|^(4)vecb`
    D
    None of these

  • Vector veca is prepedicular to vecb , componets of veca- vecb along veca + vecb will be :

    A
    zero
    B
    a-b
    C
    `(a^(2)- b^(2))/(sqrt(a^(2)+ b^(2)))`
    D
    `sqrt(a^(2)+ b^(2))`

  • If veca, vecb are the unit vectors such that veca + 2vecb + 2vecc=0 , then |veca xx vecc| is equal to:

    A
    `1/4`
    B
    `sqrt(15)/16`
    C
    `15/16`
    D
    `sqrt(15)/4`

    • Similar Questions

    Explore conceptually related problems

    If veca and vecb are two vectors, such that |veca xx vecb|=2 , then find the value of [veca vecb veca xx vecb]

    If veca, vecb, and vecc are unit vectors such that veca +2vecb +2vecc =vec0 , then |veca xx vecc| is equal to :

    If veca , vecb are unit vectors such that the vector veca + 3vecb is peependicular to 7 veca - vecb and veca -4vecb is prependicular to 7 veca -2vecb then the angle between veca and vecb is

    If veca and vecb are othogonal unit vectors, then for a vector vecr non - coplanar with veca and vecb vector vecr xx veca is equal to

    If veca and vecb are two vectors such that veca.vecb = 0 and veca xx vecb = vec0 , then

    Home
    Profile