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Prove that [vec(a)xxvec(b)vec(b)xxvec(c ...

Prove that `[vec(a)xxvec(b)vec(b)xxvec(c )vec(c)xxvec(a)]=[vec(a)vec(b)vec(c)]^(2)`.

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ARIHANT PRAKASHAN-VECTORS -TOPIC -2 (PRACTICE QUESTIONS) (4 MARK QUESTIONS)
  1. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

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  2. If vec a, vec b, vec c are mutually perpendicular vectors of equal mag...

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  3. Prove that [vec(a)xxvec(b)vec(b)xxvec(c )vec(c)xxvec(a)]=[vec(a)vec(b)...

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  4. Prove that the following vectors can never be coplanar for any real va...

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  5. Prove the following by vector method. An angle inscribed in a semi-cir...

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  6. If vec(a),vec(b) and vec(c ) are mutually perpendicular vectors, then ...

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  7. Find a vector vec(b) such that vec(a) xx vec(b) = vec(c) and vec(a).ve...

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  8. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

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  9. The diagonals of a parallelogram are given by vec(a)=2hat(i)-3hat(j)+5...

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  10. Resolve the vector vec(b) = hat(i) + hat(j) + hat(k) into vectors para...

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  11. Prove that the following vectors are coplanar -4hat(i) + 4hat(j) + 4ha...

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  12. If the magnitude of the difference of two unit vectors is sqrt3 then f...

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  13. Find the value of t, such that the following vectors are perpendicular...

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  14. Find the unit vector perpendicular to the vectors 2hat(i)-hat(j)+hat(k...

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  15. Find |vec(a)|" and "|vec(b)|," if "(vec(a)+vec(b))*(vec(a)-vec(b))=8 a...

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  16. If vec(a)xxvec(b)=vec(c)xxvec(d) and vec(a)xxvec(c)=vec(b)xxvec(d), th...

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  17. If vec(a)=3hat(i)-2hat(j)-2hat(k) and vec(b)=2hat(i)+3hat(j)+hat(k), t...

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  18. If vec(a),vec(b)" and "vec(c) are three vectors, such that vec(a)+vec(...

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  19. Show that (vec(a)-vec(b))xx(vec(a)+vec(b))=2(vec(a)xxvec(b)).

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  20. If vec(a)=2hat(i)+hat(j)-hat(k),vec(b)=-hat(i)+2hat(j)-4hat(k),vec(c)=...

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