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Find all lambda in R such that (x,y,z)!=...

Find all `lambda in R` such that `(x,y,z)!=(0,0,0)` and `(vec i + vec j + 3 vec k) x + (3 vec i - 3 vec j + vec k) y + (-4 vec i + 5 vec j) z = lambda(x vec i + y vec j +z vec k)`.

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A DAS GUPTA-Vectors and Addition of Vectors-Exercise
  1. If O is the circumcentre and P the orthocentre of Delta ABC, prove tha...

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  2. If O is the circumcentre and P the orthocentre of Delta ABC, prove tha...

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  3. If S is circumcentre, O is orthocentre of DeltaABC, then vec(SA)+vec(...

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  4. If ABCDEF is a regular hexagon, prove that vec(AC)+vec(AD)+vec(EA)+vec...

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  5. In Fig. ABCDEF is a regular hexagon. Prove that vec(AB) +vec(AC) +ve...

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  6. Find area of the triangle formed by the points (1,2,3), (-1,-1,8) and ...

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  7. The vectors of A,B,C and D are respectively 2 vec I + 3 vec j + 5 vec ...

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  8. Find all lambda in R such that (x,y,z)!=(0,0,0) and (vec i + vec j + 3...

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  9. What is the unit vector hat a parallel to the vector vec a= 3 vec I + ...

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  10. Vectors vec a, vec b are noncollinear. Find x so that the vectors (x-...

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  11. The position vectors of the points A,B,C are vec a, vec b, vec c respe...

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  12. If three vector 2veci-vecj-veck,veci+2vecj-3veck,3veci+lambdavecj+5vec...

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  13. If vec a, vec b, vec c are three non collinear vectors then show that ...

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  14. If the points A(2,3,-4), B(1,-2,3) and C(3,lambda,-1) are colliner, th...

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  15. Show that the four point (0,-1,-1),(4,5,1),(3,9,4)a n d(-4,4,4) are co...

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  16. Three non-zero vectors vec(a), vec(b), vec(c) are such that no two of ...

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