Home
Class 12
MATHS
If vec(a), vec(b) and vec(c ) are mutual...

If `vec(a), vec(b)` and `vec(c )` are mutually perpendicular unit vectors and `vec(a)xx vec(b)=vec(c )`, show that `vec(b)=vec(c )xx vec(a)` and `vec(a)=vec(b)xx vec(c )`.

Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (i) Short Answer Type Questions|3 Videos
  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (i) Long Answer Type Questions (I)|8 Videos
  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (e ) Long Answer Type Questions (II)|4 Videos
  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

If vec a,vec b,vec c are mutually perpendicular unit vectors,find |2vec a+vec b+vec c|

If vec a and vec b and vec c are mutually perpendicular unit vectors,write the value of |vec a+vec b+vec c|

If vec a and vec b are mutually perpendicular unit vectors,write the value of |vec a+vec b+vec c|

Let vec(a), vec(b) and vec(c) be three mutually perpendicular vectors each of unit magnitud. If vec(A)=vec(a)+vec(b)+vec(c), vec(B)=vec(a)-vec(b)+vec(c) and vec(C)=vec(a)-vec(b)-vec(c) , then which one of the following is correct?

Let vec(a).vec(b) and vec(c ) be three mutually perpendicular vectors each of unit magnitude. If vec(A) = vec(a) + vec(b) + vec(c ),  vec(B) = vec(a)- vec(b) + vec(c ) and vec(C ) = vec(a) - vec(b) - vec(c ) , then which one of the following is correct?

If vec A, vec B and vec C are mutually perpendicular vectors, then find the value of vec A. vec (B + vec C) .

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)xx vec(b)=vec(c ), vec(b)xx vec(c )=vec(a) , prove that vec(a), vec(b), vec(c ) are mutually at right angles and |vec(b)|=1, |vec(c )|=|vec(a)| .

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)+vec(b)+vec(c )=0 , then prove that : vec(a)xx vec(b)=vec(b)xx vec(c )=vec(c )xx vec(a) and hence, show that [vec(a)vec(b)vec(c )]=0 .

Prove that : {(vec(b)-vec(c ))xx(vec(c )-vec(a))}.(vec(a)-vec(b))=0 .

If vec a, vec b, vec c are three mutually perpendicular vectors such that | vec a | = | vec b | = | vec c | then (vec a + vec b + vec c) * vec a =