Home
Class 12
MATHS
If veca,vecb, vecc are three vectors su...

If ` veca,vecb, vecc` are three vectors such that
` veca + vecb +vecc =vec0, |veca| =1 |vecb| =2, | vecc| =3` , then
` veca.vecb + vecb .vecc + vecc.veca ` is equal to

A

1

B

0

C

-7

D

7

Text Solution

Verified by Experts

The correct Answer is:
C
we have,
` veca + vecb + vecc = vec0`
` Rightarrow |veca + vecb + vecc | = 0`
` Rightarrow |veca + vecb + vecc|^(2) =0`
` Rightarrow |veca|^(2) + |vecb|^(2) + 2 ( veca .vecb + vecb .vecc + vecc. veca) =0`
`Rightarrow 1+4+ 9+2 ( veca .vecb +vecb .vecc + vecc .veca) = 0`
` Rightarrow veca. vecb + vecb.vecc + vecc.veca = - 7 `
Promotional Banner

Topper's Solved these Questions

  • SCALER AND VECTOR PRODUCTS OF TWO VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|12 Videos

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|63 Videos

  • SOLUTIONS OF TRIANGLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|20 Videos

Similar Questions

Explore conceptually related problems

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

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

If veca,vecbandvecc are three vectors such that veca+vecb+vecc=0and|veca|=2,|vecb|=3and|vecc|=5 , then the value of veca.vecb+vecb.vecc+vecc.veca is

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

veca,vecb,vecc are 3 vectors, such that veca+vecb+vecc=0, |veca|=1,|vecb|=2,|vecc|=3, then veca.vecb+vecb.vecc+vecc.veca is equal to (A) 0 (B) -7 (C) 7 (D) 1

If veca,vecb, vecc are three vectors such that |veca |= 5, |vecb| = 12 and | vecc|=13 and veca+vecb+vecc=0 then veca.vecb+vecb.vecc+vecc.veca is equal to

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 veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

If veca, vecb, vecc are any three vectors such that (veca+vecb).vecc=(veca-vecb)vecc=0 then (vecaxxvecb)xxvecc is

If veca +vecb +vecc =vec0, |veca| =3 , |vecb|=5 and |vecc| =7 , then the angle between veca and vecb is