Home
Class 11
PHYSICS
If veca and vecb are two non collinear u...

If `veca and vecb` are two non collinear unit vectors and `|veca+vecb|= sqrt3`, then find the value of `(veca- vecb)*(2veca+ vecb)`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)`
`because a=b = 1` so `a^(2) + b^(2) + 2ab cos theta = (sqrt3)^(2) = 3`
`rArr " "1+1 + 2cos theta = 3 rArr cos theta = (1)/(2)`
`( veca-vecb) *( 2veca+ vecb) = 2a^(2) - b^(2) - abcostheta`
`" "= 2-1- (1)/(2 )=(1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS USED IN PHYSICS &VECTORS

    ALLEN|Exercise BEGINNER S BOX 12|4 Videos

  • BASIC MATHEMATICS USED IN PHYSICS &VECTORS

    ALLEN|Exercise TRIGONOMETRY|7 Videos

  • BASIC MATHEMATICS USED IN PHYSICS &VECTORS

    ALLEN|Exercise BEGINNER S BOX 10|3 Videos

  • CENTRE OF MASS

    ALLEN|Exercise EXERCISE-V B|19 Videos

Similar Questions

Explore conceptually related problems

If veca and vecb are two non collinear unit vectors and iveca+vecbi=sqrt(3) then find the value of (veca-vecb).(2veca+vecb)

If veca and vecb are two non-collinear unit vectors and if |veca_(1) + veca_(2)|=sqrt(3) , then the value of (veca_(1) -veca_(2))(2veca_(1) +veca_(2)) is:

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

If |veca|=|vecb|=|veca+vecb|=1 then find the value of |veca-vecb|

Let veca and vecb be unit vectors such that |veca+vecb|=sqrt3 . Then find the value of (2veca+5vecb).(3veca+vecb+vecaxxvecb)

Let veca and vecb be unit vectors such that |veca+vecb|=sqrt(3) , then the value of (2veca+5vecb)*(3veca+vecb+vecaxxvecb)=

If veca and vecb be two non-collinear unit vectors such that vecaxx(vecaxxvecb)=1/2vecb then find the angle between veca and vecb .

If veca and vecb be two non-collinear unit vectors such that vecaxx(vecaxxvecb)=1/2vecb then find the angle between veca and vecb .

Let veca and vecb be unit vectors such that |veca+vecb|=sqrt(3) , then the value of (2veca+5vecb) . (3veca+vecb+vecaxxvecb)=