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Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb...

Let `veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(1)hati+b_(2)hatj+b_(3)hatk and vecc=c_(1)hati+c_(2)hatj+c_(3)hatk` be three non-zero vectors such that `vecc` is a unit vector perpendicular to both `veca and vecb`. If the angle between `veca and vecb is pi//6` then the value of `|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|"is"`

A

`1//2`

B

`1//4`

C

1

D

2

Text Solution

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The correct Answer is:
A
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Let veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(1)hati + b_(2)hatj + b_(3)hatk and vecc=c_(1)hati +c_(2)hatj +c_(3)hatk be three non-zero vectors such that vecc is a unit vector perpendicular to both vectors, veca and vecb . If the angle between veca and vecb is pi//6 "then" |{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|^(2) is equal to

Let veca=a_(1)hati+a_(2)hatj+a_(3)hatk, vecb=b_(1)hati+b_(2)hatj+b_(3)hatk and vecc=c_(1)hati+c_(2)hatj+c_(3)hatk be three non zero vectors such that vecc is a unit vector perpendicular to both veca and vecb . If the angle between veca and vecb is (pi)/6 , then |(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))|^(2) is equal to

Let veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(2)hatj+b_(3)hatk and vecc=c_(1)hati+c_(2)hatj+c_(3)hatk gve three non-zero vectors such that vecc is a unit vector perpendicular to both veca and vecb . If the angle between veca and vecb is pi/6 , then prove that |{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|p=1/4 (a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))

Let veca=a_1hati+a_2hatj+a_3hatk, vecb=b_1hati+b_2hatj+b_3hatk and vecc=c_1hati+c_2hatj+c_3hatk then show that vecaxx(vecb+vecc)=vecaxxb+vecaxxvecc

Let overset(to)(a) =a_(1) hat(i) + a_(2) hat(j) + a_(3) hat(k) , overset(to)(b) = b_(1) hat(i) +b_(2) hat(j) +b_(3) hat(k) " and " overset(to)(c) = c_(1) hat(i) +c_(2) hat(j) + c_(3) hat(k) be three non- zero vectors such that overset(to)(c ) is a unit vectors perpendicular to both the vectors overset(to)(a ) and overset(to)(b) . If the angle between overset(to)(a) " and " overset(to)(b) is (pi)/(6) then |{:(a_(1),,a_(2),,a_(3)),(b_(1),,b_(2),,b_(3)),(c_(1),,c_(2),,c_(3)):}|^2 is equal to

If veca=hati-2hatj+3hatk, vecb=2hati+3hatj-hatk and vecc=rhati+hatj+(2r-1)hatk are three vectors such that vecc is parallel to the plane of veca and vecb then r is equal to,

If veca,vecb,vecc are unit vectors such that veca is perpendicular to vecb and vecc and |veca+vecb+vecc|=1 then the angle between vecb and vecc is (A) pi/2 (B) pi (C) 0 (D) (2pi)/3

Let veca=hati+hatj-hatk, vecb=hati-hatj+hatk and vecc be a unit vector perpendicular to veca and coplanar with veca and vecb , then it is given by

If two vectors are given as veca = hati - hatj + 2hatk and vecb = hati + 2hatj+hatk , the unit vector perpendicular to both vec a and vec b is

If veca=2hati-hatj+hatk and vecb=3hati+4hatj-hatk , prove that vecaxxvecb represents a vector which perpendicular to both veca and vecb .

VMC MODULES ENGLISH-VECTORS -LEVEL -2
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  2. If veca, vecb and vecc be three non-coplanar vectors and a',b' and c' ...

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  3. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(1)hati+b(2)hatj+b(3)hatk an...

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  5. If I is the centre of a circle inscribed in a triangle ABC, then |vec...

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  6. Let hata and hatb be mutually perpendicular unit vectors. Then for an...

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  7. Let veca, vecb,vecc be unit vectors, equally inclined to each other at...

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  8. Let veca,vecb,vecc be three non coplanar and vecdbe a vector which is ...

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  9. If veca, vecb, vecc are unit vectors, then |veca-vecb|^2+|vecb-vecc|^2...

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  10. Let veca, vecb and vecc be three non- coplanar vectors and vecr be any...

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  11. If vecu and vecv be unit vectors. If vecw is a vector such that vecw+(...

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  12. When a right handed rectangular Cartesian system OXYZ is rotated about...

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  13. If veca, vecb, vecc are three non-coplanar vectors, then a vector vecr...

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  14. Given a cube ABCD A(1)B(1)C(1)D(1) which lower base ABCD, upper base A...

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  15. Let veca, vecb, vecc be three non-zero non coplanar vectors and vecp, ...

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  16. If veca, vecb, vecc are unit vectors such that veca. vecb=0, (veca-vec...

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  17. I' is the incentre of DeltaABC whose corresponding sides are a,b,c res...

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  18. Consider a tetrahedron with faces F(1),F(2),F(3),F(4). Let vec(V(1)), ...

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  19. find all the possible triplets (a(1), a(2), a(3)) such that a(1)+a(2) ...

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  20. In triangle ABC if bar(AB) =u/(|bar u|)-v/(|bar v|) and bar(AC)=(2bar...

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