Home
Class 12
MATHS
Prove that : (vec(b)+vec(c )).{(vec(...

Prove that :
`(vec(b)+vec(c )).{(vec(c )+vec(a))xx(vec(a)+vec(b))}=2 [vec(a)vec(b)vec(c )]`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (j) Long Answer Type Questions (II)|1 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise Objective Type Questions (A. Multiple Choice Questions)|40 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (j) Short Answer Type Questions|17 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

Prove that : {(vec(b)+vec(c ))xx(vec(c )+vec(a))}.(vec(a)+vec(b))=2[vec(a)vec(b)vec(c )]

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

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

Prove that: [vec(a)" "vec(b)" "vec( c )+vec(d)]=[vec(a)" "vec(b)" "vec( c )]+[vec(a)" "vec(b)" "vec(d)] .

For any three vectors vec(A), vec(B) and vec(C) prove that vec(A) xx (vec(B) +vec(C)) +vec(B) xx (vec(C) +vec(A)) + vec(C) xx (vec(A) +vec(B)) = vec(O)

[vec(a)vec(b)vec(c )]=[vec(b)vec(c )vec(a)]=[vec(c )vec(a)vec(b)] .

If vec(a).vec(b)xx vec(c ) ≠ 0 and vec(a')=(vec(b)xx vec(c ))/(vec(a).vec(b)xx vec(c )), vec(b')=(vec(c )xx vec(a))/(vec(a).vec(b)xx vec(c )), vec(c')=(vec(a)xx vec(b))/(vec(a).vec(b)xx vec(c )) , show that : vec(a').(vec(b')xx vec(c'))=(1)/(vec(a).(vec(b)xx vec(c )))

If vec(a).vec(b)xx vec(c )≠0 and vec(a')=(vec(b)xx vec(c ))/(vec(a).vec(b)xx vec(c )), vec(b')=(vec(c )xx vec(a))/(vec(a).vec(b)xx vec(c )), vec(c')=(vec(a)xx vec(b))/(vec(a).vec(b)xx vec(c )) , show that : vec(a).vec(a')+vec(b).vec(b')+vec(c ).vec(c')=3

If vec(a).vec(b)xx vec(c ) ≠ 0 and vec(a')=(vec(b)xx vec(c ))/(vec(a).vec(b)xx vec(c )), vec(b')=(vec(c )xx vec(a))/(vec(a).vec(b)xx vec(c )), vec(c')=(vec(a)xx vec(b))/(vec(a).vec(b)xx vec(c )) , show that : vec(a).vec(a')+vec(b). vec(b')+vec(c ). vec(c')=3 .