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If vec(d)=vec(a)xx(vec(b)xxvec(c))+vec(b...

If `vec(d)=vec(a)xx(vec(b)xxvec(c))+vec(b)xx(vec(c)xxvec(a))+vec(c)xx(vec(a)xxvec(b))," then "`

A

`absvec(d)=1`

B

`vec(d)=vec(a)+vec(b)+vec(c)`

C

d = 0

D

a, b, c are coplanar

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The correct Answer is:
D
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SURA PUBLICATION-APPLICATIONS OF VECTORA ALGEBRA-ADDITIONAL QUESTIONS ( Choose the Correct or the most suitable answer from the given four alternatives : )
  1. Let vec(a),vec(b)andvec(c) be three non-coplanar vectors and let vec(p...

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  2. The number of vectors of unit length perpedicular to the vectors (ha...

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  3. If vec(d)=vec(a)xx(vec(b)xxvec(c))+vec(b)xx(vec(c)xxvec(a))+vec(c)xx(v...

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  4. If vec(a)andvec(b) are two unit vectors, then the vectors (vec(a)+vec(...

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  5. The area of the parallelogram having diagonals vec(a)=3hat(i)+hat(j)-2...

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  6. If vec(a),vec(b)andvec(c) are any three vectors, then vec(a)xx(vec(b)x...

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  7. The volume of the parallelepiped whose sides are given by bar(OA)=2hat...

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  8. If absvec(a)=absvec(b)=1" such that "vec(a)+2vec(b)and5vec(a)-4vec(b) ...

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  9. The angle between the vector 3hat(i)+4hat(j)+5hat(k) and the z-axis is

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  10. A vector vec(OP) makes 60^(@) and 45^(@) with the positive direction o...

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  11. If vec(a)=hat(i)+2hat(j)+3hat(k),vec(b)=-hat(i)+2hat(j)+hat(k),vec(c)=...

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  12. If theta is the between the vector vec(a)andvec(b)," then " sintheta i...

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  13. If the vectors hat(i)+hat(j)+2hat(k),-hat(i)+2hat(k)and2hat(i)+xhat(j)...

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  14. If vec(a)=absvec(a)vec(e)" then "vec(e).vec(e) is

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  15. The value of |vec(a)+vec(b)|^(2)+|vec(a)-vec(b)|^(2) is

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  16. If vec(p)xxvec(q)=2hat(i)+3hat(j),vec(r)xxvec(s)=3hat(j)+2hat(k)," the...

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  17. If the work done by a force bar(F)=hat(i)+mhat(j)+hat(k) in moving the...

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  18. The two planes 3x + 3y - 3z - 1 = 0 and x + y - z + 5 = 0 are

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  19. The straight lines (x-3)/(2)=(y+5)/(4)=(z-1)/(-13)and(x+1)/(3)=(y-4)/(...

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  20. For what value of (vec(a)) will the straight lines (x+2)/(2)=(y)/(-3)=...

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