Home
Class 12
MATHS
Let vec a , vec b and vec c be unit vec...

Let ` vec a , vec b` and `vec c` be unit vectors such that ` vec a+ vec b- vec c=0.` If the area of triangle formed by vectors ` vec a and vec b` is `A ,` then what is the value of `4A^2?`

Text Solution

Verified by Experts

The correct Answer is:
3
Given a+b=c
Now, vector c is along the diagonal of the parallelogram which has adjacent side vectors a and b. sincne, c is also a unit vector, triangle formed by vectors a and b is an equilateral triangle.
Then, area of triangle `=(sqrt(3))/(4)impliesA^(2)=(3)/(10)implies16A^(2)=3`.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|17 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|19 Videos

Similar Questions

Explore conceptually related problems

vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c=0. then find the value of vec a. vec b+ vec b.vec c+ vec c. vec a

If vec a , vec b ,a n d vec c are unit vectors such that vec a+ vec b+ vec c=0, then find the value of vec adot vec b+ vec bdot vec c+ vec cdot vec adot

If vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c= vec0, then write the value of vec a . vec b+ vec b . vec c+ vec c . vec a

If vec a ,\ vec b ,\ vec c are unit vectors such that vec a+ vec b+ vec c= vec0 find the value of vec adot vec b+ vec bdot vec c+ vec cdot vec adot'

Let vec a , vec b , vec c be the three unit vectors such that vec a+5 vec b+3 vec c= vec0 , then vec a. ( vec bxx vec c) is equal to

If veca , vec b , vec c are three vectors such that veca+ vec b+ vec c= vec0 , then prove that vec axx vec b= vec bxx vec c= vec cxx vec a

Let vec a , vec b , vec c be unit vectors such that vec adot vec b= vec adot vec c=0 and the angle between vec ba n d vec c is pi/6,t h a t vec a=+-2( vec bxx vec c)dot

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

If vec a , vec b , vec c are unit vectors such that vec a. vec b=0= vec a. vec c and the angle between vec b and vec c is pi/3, then find the value of | vec axx vec b- vec axx vec c| .

Let vec a , vec b and vec c be three non-zero vectors such that vec a+ vec b+ vec c=0 and lambda vec bxx vec a+ vec bxx vec c+ vec cxx vec a=0, then find the value of lambda