Home
Class 12
MATHS
If vecb is not perpendicular to vecc . T...

If `vecb` is not perpendicular to `vecc` . Then find the vector `vecr` satisfying the equation `vecr xx vecb = veca xx vecb and vecr. vecc=0`

Text Solution

Verified by Experts

Given `vecrxxvecb=vecaxxvecbRightarrow (vecr-veca)xxvecb=0`
Hence, (`vecr - veca) and vecb` are parallel.
`Rightarrow vecr-veca=tvecb`
`vecr.vecc=0`
Therefore, taking dot product of (i) by `vecc`, we get `vecr.vecc -veca.vecc=t(vecb .vecc)`
`or 0-veca.vecc=r(vecb.vecc)ort=-((veca.vecc)/(vecb.vecc))`
from (i) and (ii) solution of `vecr" is " vecr =veca-((veca.vecc)/(vecb.vecc))vecb`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.1|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.2|15 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

Let veca and vecb be two non- zero perpendicular vectors. A vector vecr satisfying the equation vecr xx vecb = veca can be

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

If vecA=(1,1,1) and vecC=(0,1,-1) are given vectors then find a vector vecB satisfying equations vecAxxvecB=vecC and vecA.vecB=3

Let veca=-hati-hatk,vecb =-hati + hatj and vecc = i + 2hatj + 3hatk be three given vectors. If vecr is a vector such that vecr xx vecb = vecc xx vecb and vecr.veca =0 then find the value of vecr .vecb .

If non-zero vectors veca and vecb are perpendicular to each other, then the solution of the equation vecr × veca = vecb is given by

Let vecr be a unit vector satisfying vecr xx veca = vecb, " where " |veca|= sqrt3 and |vecb| = sqrt2 , then

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) =

If veca = hati + hatj + hatk , vecb = hatj - hatk then find a vector vecc , such that veca xx vecc = vecb and veca .vecc = 3 .

If veca .vecb =beta and veca xx vecb = vecc ," then " vecb is