Home
Class 12
MATHS
Prove that if the vectors vec a, vec b, ...

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`

Text Solution

Verified by Experts

The correct Answer is:
`vec a xx vec b = vec b xx vec c = vec c xx vec a`
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

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

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

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] .

Prove that vec a xx (vec b + vec c) + vec b xx(vec a + vec c)+ vec c xx(vec a + vec b) = vec 0

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.

If three unit vectors vec a , vec b ,a n d vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec aa n d vec bdot

The length of the perpendicular form the origin to the plane passing through the point a and containing the line vec r= vec b+lambda vec c is a. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|) b. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c|) c. ([ vec a vec b vec c])/(| vec bxx vec c+ vec cxx vec a|) d. ([ vec a vec b vec c])/(| vec cxx vec a+ vec axx vec b|)

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)

Prove that [ vec a, vec b, vec c + vec d] = [ vec a, vec b, vec c] + [ vec a, vec b , vec d] .

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a