Home
Class 12
MATHS
If veca, vecb are unit vectors such tha...

If ` veca, vecb` are unit vectors such that ` |veca +vecb|=1 and |veca -vecb|=sqrt3`, " then " `|3veca +2vecb|=`

A

7

B

4

C

` sqrt7`

D

`sqrt19`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `theta` the angle between `veca and vecb` . Then,
` tan "" theta/2= (|veca -vecb|)/(|veca +vecb|) Rightarrow tan "" theta/2 = sqrt3 Rightarrow theta =120^(@)`
` veca.vecb = |veca||vecb| cos theta =cos 120^(@) = -1/2`
Now ,
` |3 veca = 2vecb|^(2) = 9 |veca|^(2) + 4 |vecb|^(2) + 12(veca .vecb)`
` Rightarrow |3veca + 2veca|^(2) = 9 +4+12 xx ( - 1/2) =7`
` Rightarrow |3veca +2vecb|= sqrt7`
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 are unit vectors such that |vec a+vecb|=-1 " then " |2veca -3vecb| =

If veca,vecb are two unit vectors such that |veca + vecb| = 2sqrt3 and |veca -vecb|=6 then the angle between veca and vecb , is

If veca and vecb are non - zero vectors such that |veca + vecb| = |veca - 2vecb| then

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

If veca and vecb are unit vectors, then the greatest value of |veca +vecb|+ |veca -vecb| is

If veca, vecb are unit vertors such that veca -vecb is also a unit vector, then the angle between veca and vecb , is

If veca , vecb are unit vectors such that the vector veca + 3vecb is peependicular to 7 veca - vecb and veca -4vecb is prependicular to 7 veca -2vecb then the angle between veca and vecb is

Let veca and vecb be two vectors such that |2 veca + 3 vecb| = |3 veca + vecb| and the angle between veca and vecb is 60^(@) . If 1/8 veca is a unit vector, then |vecb| is equal to :

If veca " and " vecv are the two vectors such that |veca| = 3sqrt3,|vecb| = 4 " and " |veca + vecb|= sqrt7 , then the anlge between veca and vecb is

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