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bar(a)=2hati+hatj-2hatk and bar(b)=hati+...

`bar(a)=2hati+hatj-2hatk` and `bar(b)=hati+hatj`. The vector `bar( c )` is such that `bar(a)*bar( c )=|bar( c )|,|bar( c )-bar(a)|=2sqrt(2)` and the angle between `bar(a)xx bar(b)` and `bar( c )` is `30^(@)` then `|(bar(a)xx bar(b))xx bar( c )|` = …………

A

`(2)/(3)`

B

`(3)/(2)`

C

2

D

3

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The correct Answer is:
B
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bar(a),bar(b) and bar( c ) are unit vectors. bar(a).bar(b)=0=bar(a).bar( c ) and the angle between bar(b) and bar( c ) is (pi)/(3) . Then |bar(a)xx bar(b)-bar(a)xx bar( c )|= …………..

bar(a),bar(b) and bar( c ) are three unit vectors. bar(a)_|_bar(b) and bar(a)||bar( c ) then bar(a)xx(bar(b)xx bar( c )) = …………….

bar(a)xx[bar(a)xx(bar(a)xx bar(b))] = …………….

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

(bar(a)xx bar(b))^(2) = ……………..

For three vectors bar(a),bar(b) and bar( c ),bar(a)xx(bar(b)xx bar( c ))=(bar(a)xx bar(b))xx bar( c ) then

[bar(a)xx bar(b)" "bar(a)xx bar( c )" "bar(d)] = …………….

If bar(x)=(1,-1,0),bar(y)=(0,1,3) and bar(z)=(2,1,1) then bar(x)xx (bar(y)xx bar(z)) = ………….

If bar(a),bar(b),bar( c ) and bar(d) are coplanar vectors then (bar(a)xx bar(b))xx(bar( c )xx bar(d)) = …………..

KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Multiple Choice Questions (MCQs) )
  1. If bar(mu)=hati xx(bar(a)xx hati)+hatj xx(bar(a)xx hatj))+hatk xx(bar(...

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  2. bar(a),bar(b) and bar( c ) are three unit vectors. bar(a)|bar(b) and b...

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

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  4. The vectors bar(a) and bar(b) are perpendicular then bar(a)xx{bar(a)xx...

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  5. If bar(a),bar(b),bar( c ) and bar(d) are coplanar vectors then (bar(a)...

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  6. bar(a)xx[bar(a)xx(bar(a)xx bar(b))] = …………….

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  7. For three vectors bar(a),bar(b) and bar( c ),bar(a)xx(bar(b)xx bar( c ...

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  8. If bar(a)=hati+hatj+hatk,bar(b)=hati+hatj,bar( c )=hati and (bar(a)xx ...

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  9. [bar(a)xx bar(b)" "bar(a)xx bar( c )" "bar(d)] = …………….

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  10. If (bar(a)xx bar(b))xx(bar(b)xx bar( c ))=bar(b), where bar(a),bar(b),...

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  11. If bar(a),bar( c ) and bar(d) are not coplanar vectors and bar(d).(bar...

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  12. If 4bar(a)+5bar(b)+9bar( c )=0 then (bar(a)xx bar(b))xx[(bar(b)xx bar(...

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  13. vec(a),vec(b) and vec( c ) are non zero vectors. (vec(a)xx vec(b))xx v...

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  14. If vec(a) is a unit vector and vec(b)=(2,1,-1) and vec( c )=(1,0,3). T...

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  15. The volume of the parallelepiped with edges -12hati+alpha hatk,3hatj-h...

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  16. bar(a)xx[bar(a)xx(bar(a)xx bar(b))] = …………….

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  17. vec(a)|vec(b) and vec(c),|vec(a)|=2,|vec(b)|=3,|vec( c )|=4. The angle...

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  18. (vec(a)xx vec(b))xx vec( c )=vec(a)xx(vec(b)xx vec( c )). If vec(a)*ve...

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  19. vec(u),vec(v) and vec(w) are not co-planar vectors and p and q are rea...

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  20. Let vec(X),vec(Y) and vec(Z) be three vectors such that |vec(X)|=|vec(...

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