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A(-1, 2, 3), B(1, 1, 1) and C(2, -1, 3) ...

A(-1, 2, 3), B(1, 1, 1) and C(2, -1, 3) are three points in the plane. The unit vector perpendicular to the plane ABC is …………..

A

`+-((2hati+2hatj+hatk)/(3))`

B

`+-((2hati-2hatj+hatk)/(3))`

C

`+-((2hati-2hatj-hatk)/(3))`

D

`-((2hati+2hatj+hatk)/(3))`

Text Solution

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The correct Answer is:
A
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bar(a)=a_(1)hati+a_(2)hatj+a_(3)hatk,bar(b)=b_(1)hati+b_(2)hatj+b_(3)hatk,bar( c )=c_(1)hati+c_(2)hatj+c_(3)hatk are three non zero vectors. The unit vector bar( c ) is perpendicular to bar(a) and bar(b) . The angle between bar(a) and bar(b) is (pi)/(6) then, |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| = .............

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KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Multiple Choice Questions (MCQs) )
  1. If |bar(x)|=7.|bar(y)|=sqrt(2),bar(x)xx bar(y)=(6,2,3) then |bar(x).ba...

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  2. The unit vector perpendicualr to both the vectors hati+2hatj-2hatk and...

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  3. A(-1, 2, 3), B(1, 1, 1) and C(2, -1, 3) are three points in the plane....

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  4. If |bar(a).bar(b)|=3 and |bar(a)xx bar(b)|=4 then the angle between ba...

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  5. bar( r )xx bar(a)=bar(b)xx bar(a),bar( r )xx bar(b)=bar(a)xx bar(b),ba...

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  6. (bar(a)xx bar(b))^(2) = ……………..

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  7. |bar(a)|=2,|bar(b)|=3 and bar(a) and bar(b) are perpendicular to each ...

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  8. bar(a)=hati+hatj+hatk,bar(b)=hati+3hatj+5hatk and bar( c )=7hati+9hatj...

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  9. In DeltaABC, the bisector of angleA is bar(AD). bar(AD)=alpha bar(AB...

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  10. The vector bar(a)=(x,y,z) makes an obtuse angle with y- axis. bar(b)=(...

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  11. The vectors bar(a) and bar(b) are unit vectors perpendicular to each o...

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  12. bar(a),bar(b) and bar( c ) are unit vectors. bar(a).bar(b)=0=bar(a).ba...

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  13. The modulus of the vectors bar(a) and bar(b) are 2 and 3 respectively....

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  14. For a vector bar(a),bar(a)xx vec( r )=bar(j) then bar(a).bar( r ) = ……...

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  15. If bar(mu)=bar(a)-bar(b),bar(v)=bar(a)+bar(b),|bar(a)|=|bar(b)|=2 then...

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  16. In a parallelogram ABCD, vec(AB)=hati+hatj+hatk and diagonal vec(AC)=h...

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  17. The points A(vec(a)),B(vec(b)) and C(vec( c )) are collinear then …………...

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  18. For any vectors vec(a),vec(b) and vec( c ). Out of the following, whic...

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  19. bar(a)=2hati+hatj-2hatk and bar(b)=hati+hatj. The vector bar( c ) is s...

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  20. In a quadrilateral ABCD, vec(AB)=vec(b),vec(AD)=vec(d) and vec(AC)=m v...

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