Home
Class 12
MATHS
Angle between vectors veca and vecb " ...

Angle between vectors ` veca and vecb " where " veca,vecb and vecc` are unit vectors satisfying ` veca + vecb + sqrt3 vecc = vec0` is

A

` pi/6`

B

`pi/4`

C

`pi/3`

D

` pi/2`

Text Solution

Verified by Experts

The correct Answer is:
C
we have,
` veca + vecb + sqrt3 vecc = vec0`
` Rightarrow veca | vecb = sqrt3 vecc`
` Rightarrow |veca + vecb| = sqrt3 |vecc|`
` Rightarrow |veca + vecb|^(2) =3 |vecc|^(2) `
` Rightarrow |veca|^(2) +|vecb|^(2) + 2|veca||vecb| cos theta =3 |veca|^(2) `
where ` theta ` is the angle between ` veca and vecb` .
` Rightarrow 1 +1 + 2 cos theta =3 Rightarrow = 1/2 Rightarrow theta = pi/3`
Promotional Banner

Topper's Solved these Questions

  • SCALER AND VECTOR PRODUCTS OF TWO VECTORS

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

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA|Exercise Exercise|65 Videos

  • SOLUTIONS OF TRIANGLES

    OBJECTIVE RD SHARMA|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 xx vecb) xx vecc = vec a xx (vecb xx vecc) , where veca, vecb and vecc are any three vectors such that veca.vecb ne 0, vecb.vecc ne 0 , then veca and vecc are:

If (veca xx vecb) xx vecc = veca xx (vecb xx vecc) where veca, vecb and vecc are any three vectors such that veca.vecb =0, vecb.vecc=0 then veca and vecc are:

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca, |veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: If vecc is a unit vector and equal to the sum of veca and vecb the magnitude of difference between veca and vecb is (A) 1 (B) sqrt(2) (C) sqrt(3) (D) 1/sqrt(2)

Let veca ,vecb , vecc be three unit vectors such that angle between veca and vecb is alpha , vecb and vecc " is " beta and vecc and veca " is " gamma. " if " | veca. + vecb + vecc| =2 , then cos alpha + cos beta + cos beta =

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca,|veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: If vecc is as unit vector such that veca.vecb=veca.vecc=0 and theta= (pi/6) then veca= (A) +-1/2(vecbxxvecc) (B) +-(vecbxxvecc) (C) +-2(vecbxxvecc) (D) none of these

Three vectors veca,vecb and vecc satisfy the relation veca.vecb=0 and veca.vecc=0 . The vector veca is parallel to

If (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) where veca, vecb and vecc are any three vectors such that veca.vecb!=0, vecb. vecc!=0 then veca and vecc are