Home
Class 12
MATHS
If vec a ,\ vec b ,\ vec c be the vec...

If ` vec a ,\ vec b ,\ vec c` be the vectors represented by theside sof a triangle, taken in order, then prove that ` vec a+ vec b+ vec c= vec0dot`

Text Solution

Verified by Experts

Let ABC be a triangle such that
BC=a,CA=b and AB=c

Then, a+b+c=BC+CA+AB `(becauseBC+CA=BA)`
`=-AB+AB`
a+b+c=0 Hence proved.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 2|17 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

Prove that [vec a -vec b, vec b - vec c, vec c- vec a] =0

If vec a , vec b , and vec c are mutually perpendicular vectors of equal magnitudes, then find the angle between vectors vec a and vec a+ vec b+ vec c dot

Let vec a , vec b , vec c are three non-zero vectors such that vec axx vec b= vec ca n d vec bxx vec c= vec a ; prove that vec a , vec b , vec c are mutually at righ angles such that | vec b|=1a n d| vec c|=| vec a|dot

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

If veca , vec b , vec c are the position vectors of the vertices A ,B ,C of a triangle A B C , show that the area triangle A B Ci s1/2| vec axx vec b+ vec bxx vec c+ vec cxx vec a|dot Deduce the condition for points veca , vec b , vec c to be collinear.

If vec a , vec b and vec c are three proper vectors such that vec a * vec b=vec c , vec b*vec c=vec a . Prove that vec a , vec b , vec c are mutually at right angles and |quad vec b|=1 ,|quad vec c|=|quad vec a|.

If vec a , vec b ,a n d vec c are three non-coplanar vectors, then find the value of ( vec adot( vec bxx vec c))/( vec b dot( vec cxx vec a))+( vec b dot( vec cxx vec a))/( vec c dot( vec axx vec b))+( vec c dot( vec bxx vec a))/( vec a dot( vec bxx vec c))dot

Let vec a , vec b , vec c , be three non-zero vectors. If vec a .(vec bxx vec c)=0 and vec b and vec c are not parallel, then prove that vec a=lambda vec b+mu vec c ,w h e r elambda are some scalars dot

If vec a , vec b , vec c are three non-coplanar vectors and vec d* vec a = vec d* vec b= vec d* vec c= 0 then show that vec d is zero vector.

If vec a , vec b are any two vectors, then give the geometrical interpretation of relation | vec a+ vec b|=| vec a- vec b|