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Show that (veca+vecb).(vecb+vec(c))xx(ve...

Show that `(veca+vecb).(vecb+vec(c))xx(vec(c)+veca)=2[a" b c"]`.

Text Solution

Verified by Experts

The correct Answer is:
`2[vecavecbvec(c)]`.
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Show that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb)

veca,vecb,vec(c) and vecd are the position vectors of four complanar points such that (veca-vecd).(vecb-vec(c))=(vecb-vecd).(vec(c)-veca)=0 . Show that the point vecd represents the orthocentre of the triangle with veca,vecb and vec(c) as its vertices.

If the vectors vec(a), vec(b), vec(c ) form the sides vec(BC), vec(CA), vec(AB) respectively of triangle ABC then show that vec(a) xx vec(b) = vec(b)xx vec(c ) = vec(c ) xx vec(a) .

If veca+vecb+vec(c)=vec0 , then prove that vecaxxvecb=vecbxxvec(c)=vec(c)xxveca .

Show that [(vec(a)xxvec(b))xx(vec(a)xxvec(c)))].vec(d)=(veca.vecd)[vecavecbvec(c)] .

If vec(a) + 2vec(b) + 4vec(c ) = vec(0) then show that vec(a) xx vec(b) =4 (vec(b) xx vec(c ))= 2(vec(c ) xx vec(a))

If veca,vecb,vec(c) are non-coplanar, then show that the vectors veca-vecb,vecb+vec(c),vec(c)+vec(a) are planar.

(vec(a) + vec(b)) xx (vec(a)-vec(b)) + (vec(b) + vec(c )) xx (vec(b)-vec(c )) + (vec(c )+ vec(a)) xx (vec(c ) -vec(a)) =

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PRODUCT OF VECTORS-EXERCISE 5(c) II
  1. If [vecb" "vec(c)" "vecd]+[vec(c)" "vec(a)" "vecd]+[vec(a)" "vecb" "ve...

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  2. It a,b and c are non-coplanar vectors and the four points with positio...

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  3. veca,vecb and vec(c) are non-zero and non-collinerr vectors and thetan...

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  4. Find the volume of the tetrahedron, whose vertices are (1,2,1), (3,2,5...

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  5. Show that (veca+vecb).(vecb+vec(c))xx(vec(c)+veca)=2[a" b c"].

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  6. Show that the equation of plane passing through the points with positi...

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  7. Prove that vecaxx[vecaxx(vecaxxvecb)]=(veca.veca)(vecbxxveca).

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  8. If veca,vecb,vecc,vecd are coplaner vectors, then (vecaxxvecb)xx(veccx...

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  9. Show that [(vec(a)xxvec(b))xx(vec(a)xxvec(c)))].vec(d)=(veca.vecd)[vec...

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  10. Show that vec(alpha).[(vec(beta)+vec(chi)xx(vec(alpha)+vec(beta)+vec(c...

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  11. Find lambda in order that the four points A(3,2,1), B(4, lambda,5),C(4...

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  12. Find the vector equation of the plane passing through the intersection...

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  13. Find the equation of the plane passing through (a,b,c) and parallel to...

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  14. Find the shortest distance between the lines and ...

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  15. Prove that the four points 4bari + 5barj +bark, - (barj + bark) , 3b...

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  16. If veca,vecb,vec(c) are non-coplanar, then show that the vectors veca-...

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  17. If veca,vecb,vec(c) are the position vectors of the points A,B and C r...

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