Home
Class 12
MATHS
If veca,vecbandvecc are unit vectors suc...

If `veca,vecbandvecc` are unit vectors such that `veca+vecb+vecc=0`, then the value of `veca.vecb+vecb.vecc+vecc.veca` is

Text Solution

Verified by Experts

squaring `(veca+vecb+vecc)= vec0` we get
`|veca|^(2)+|vecb|^(2)=|vecc|^(2)+2 veca.vecb+ 2vecb.vecc + 2vecc.veca=0`
`2(veca.vecb+vecb.vecc+vecc.veca)=-3`n
`veca.vecb+vecb.vecc+vecc.veca= -3/2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.1|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.2|15 Videos

  • DETERMINANTS

    CENGAGE ENGLISH|Exercise All Questions|264 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

Similar Questions

Explore conceptually related problems

If veca,vecb and vecc are unit vectors such that veca+vecb+vecc=vec0 then the value of veca.vecb+vecb.vecc+vecc.veca is a) 1 b) 0 c) 3 d) -3/2

If veca,vecb and vecc are unit vectors such that veca + vecb + vecc= 0 , then prove that veca.vecb+vecb.vecc+vecc.veca=-3/2

If veca , vecb , vecc are unit vectors such that veca+ vecb+ vecc= vec0 find the value of (veca* vecb+ vecb* vecc+ vecc*veca) .

If veca,vecb,vecc are three unit vectors such that veca+vecb+vecc=0, then veca.vecb+vecb.vecc+vecc.veca is equal to (A) -1 (B) 3 (C) 0 (D) -3/2

if veca , vecb ,vecc are three vectors such that veca +vecb + vecc = vec0 then

If veca, vecb, vecc are three non-zero vectors such that veca + vecb + vecc=0 and m = veca.vecb + vecb.vecc + vecc.veca , then:

If two out to the three vectors , veca, vecb , vecc are unit vectors such that veca + vecb + vecc =0 and 2(veca.vecb + vecb .vecc + vecc.veca) +3=0 then the length of the third vector is

For any three vectors veca, vecb, vecc the value of [(veca-vecb, vecb-vecc, vecc-veca)] , is

If veca, vecb, vecc are vectors such that veca.vecb=0 and veca + vecb = vecc then:

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