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Prove that (vec a × vec b)^(2) = a^(2)b^...

Prove that `(vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2)`.

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The correct Answer is:
`[becausevec(a)*vec(b)=|vec(a)||vec(b)|costheta,0lethetaltpi]`
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Show that (vec(a) xx vec(b))^(2) = |(vec(a).vec(a), vec(a).vec(b)),(vec(a).vec(b), vec(b).vec(b))| .

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

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

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ARIHANT PRAKASHAN-VECTORS -TOPIC -2 (PRACTICE QUESTIONS) (4 MARK QUESTIONS)
  1. Find a unit vector perpendicular to each of the vectors vec(a) + vec(b...

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  2. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

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  3. Prove that for any three vectors vec(a), vec(b) and vec(c), [vec(a) + ...

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  4. Show that hat(i) xx (vec(a) xx hat(i)) + hat(j) xx (vec(a) xx hat(j)) ...

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  5. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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