Home
Class 12
MATHS
Show that the vectors vec a, vec b and v...

Show that the vectors `vec a, vec b` and `vec c` are coplanar if `vec a + vec b, vec b + vec c, vec c+ vec a` are coplanar.

Text Solution

Verified by Experts

The correct Answer is:
Hence `[ vec a, vec b, vec c] = 0 therefore vec a, vec b and vec c` are coplanar.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    NEW JOYTHI PUBLICATION|Exercise SOLUTIONS TO NCERT TEXT BOOK EXERCISE 10.1|4 Videos

  • VECTOR ALGEBRA

    NEW JOYTHI PUBLICATION|Exercise SOLUTIONS TO NCERT TEXT BOOK EXERCISE 10.1 (Answer the following as true or false )|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|134 Videos

Similar Questions

Explore conceptually related problems

Show that for any three vectors veca , vec b and vec c [ vec a + vec b, vecb + vec c , vec c + vec a ] =2[vec a , vec b , vecc] .

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=0

If vec a , vec b and vec c are non-coplanar vectors, prove that vectors 3vec a-7 vec b-4 vec c ,3 vec a -2 vec b+ vec c and vec a + vec b +2 vec c are coplanar.

If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c are nonzero vectors, then (a) vec a , vec b ,a n d vec c can be coplanar (b) vec a , vec b ,a n d vec c must be coplanar (c) vec a , vec b ,a n d vec c cannot be coplanar (d)none of these

Prove that if the vectors vec a, vec b, vec c satisfy vec a+ vec b + vec c = vec 0 , then vec bxx vec c = vec c xx vec a = vec a xx vec b

If vec a , vec b , vec c ,a n d vec d are four non-coplanar unit vector such that vec d make equal angles with all the three vectors vec a , vec ba n d vec c , then prove that [ vec d vec a vec b]=[ vec d vec c vec b]=[ vec d vec c vec a]dot

For any three vectors vec a, vec b , vec c , show that vec a xx (vec b + vec c) + vec b xx (vec c + vec a) + vec c xx (vec a + vec b) = 0