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

If `vec(a)xx(vec(b)xxvec(c))=(vec(a)xxvec(b))xxvec(c)," where "vec(a),vec(b)vec(c)` are any three vectors such that `vec(b)*vec(c)ne0andvec(a)*vec(b)ne0," then "vec(a)andvec(c)" are "`

A

perpendicular

B

parallel

C

inclined at an angle`(pi)/(3)`

D

inclined at an angle`(pi)/(6)`

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The correct Answer is:
A, B, C, D
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SURA PUBLICATION-APPLICATIONS OF VECTORA ALGEBRA-EXERCISE 6.10 (Choose the Correct or the most suitable answer from the given four alternative : )
  1. The volume of the parallelepiped with its edges represented by the vec...

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  2. If vec(a)andvec(b) are unit vectors such that [vec(a),vec(b),vec(a)xxv...

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  3. If vec(a)=hat(i)+hat(j)+hat(k),vec(b)=hat(i)+hat(j),vec(c)=hat(i)and(v...

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  4. If vec(a),vec(b),vec(c) are non-coplanar, non-zero vectors such that [...

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  5. If vec(a),vec(b),vec(c) are three non-coplanar vectors such that vec(a...

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  6. If the volume of the parallelpiped with vec(a)xxvec(b),vec(b)xxvec(c),...

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  7. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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  8. If vec(a)xx(vec(b)xxvec(c))=(vec(a)xxvec(b))xxvec(c)," where "vec(a),v...

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  9. If vec(a)=2hat(i)+3hat(j)-hat(k),vec(b)=hat(i)+2hat(j)-5hat(k),vec(c)=...

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  10. The angle between the lines (x-2)/(3)=(y+1)/(-2),z=2and(x-1)/(1)=(2y+3...

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  11. If the line (x-2)/(3)=(y-1)/(-5)=(z+2)/(2)" lies in the plane "x+3y-az...

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  12. The angle between the lines vec(r)=(hat(i)+2hat(j)-3hat(k))+t(2hat(i)+...

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  13. The coordinates of the point where the line vec(r)=(6i-j-3k)+t(-i+4k)"...

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  14. Distance from the origin to the plane 3x - 6y + 2z + 7 = 0 is

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  15. The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z +...

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  16. If direction cosines of a line are (1)/(c),(1)/(c),(1)/(c)," then. "

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  17. The vector equation vec(r)=(hat(i)-2hat(j)-hat(k))+t(6hat(j)-hat(k)) r...

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  18. If the distance of the point (1,1,1) from the origin is half of its di...

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  19. If the planes vec(r)*(2hat(i)-lamdahat(j)+hat(k))=3andvec(r)(4hat(i)+h...

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  20. If the length of the perpendicular from the origin to the plane 2x+3y+...

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