Home
Class 12
MATHS
Three vectors veca,vecb,vecc are such th...

Three vectors `veca,vecb,vecc` are such that `veca xx vecb=4(veca xx vecc)` and `|veca|=|vecb|=1` and `|vecc|=1/4`. If the angle between `vecb` and `vecc` is `pi/3` then `vecb` is

A

`veca + 4vecc`

B

`veca-4vecc`

C

`4vecc-veca`

D

`2vecc-veca`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`veca xx vecb = 4(veca xx vecc)`
`veca xx (vecb-4vecc)=vec0`
`rArr veca = t(vecb-4vecc)`, where t is scalar.
`therefore |veca|^(2)=t^(2){|b^(2)|+16|c|^(2)-8(vecb.vecc)}`
`therefore 1=t^(2){1+16.1/16-8.1.1/4.1/2}`
`therefore 1=t^(2)[1]`
`therefore t=+-1`
`t=+-1`
`therefore veca=vecb-4vecc` or `veca=vecb+4vecc`
`rArr vecb=veca+4vec`or `vecb=4vecc-veca`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise JEE Main Previous Year|6 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

Similar Questions

Explore conceptually related problems

If veca,vecb,vecc are three vectors such that veca+2vecb+vecc=vec0 and |veca|=3,|vecb|=4,|vecc|=7 , find the angle between veca and vecb .

If veca,vecb,vecc are three vectors such that veca+2vecb+vecc=vec 0 and|veca|=3,|vecb|=4,|vecc|=7 find the angle between vecaandvecb

If veca+vecb+vecc =0, |veca|=3, |vecb|=5, |vecc|=7 then the angle between veca and vecb is :

If veca,vecb,vecc are three vectors such that veca+2vecb+vecc=vec0and|veca|=3,|vecb|=4,|vecc|=7 , find the angle between vecaandvecb .

veca+vecb+vecc=vec0, |veca|=3, |vecb|=5,|vecc|=9 ,find the angle between veca and vecc .

The vectors veca-vecb,vecb-vecc,vecc-veca are

If |veca|+|vecb|=|vecc|and veca+vecb=vecc then find the angle between veca and vecb .

Let veca, vecb, vecc be three unit vectors and veca.vecb=veca.vecc=0 . If the angle between vecb and vecc is pi/3 then find the value of |[veca vecb vecc]|

If veca, vecb,vecc are unit vectors such that veca.vecb = 0= veca.vecc and the angle between vecb and vecc is pi//3 then the value of |vecaxxvecb -veca xx vecc| is