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The vectors bar(a)=3bar(i)-2bar(j)+2bar(...

The vectors `bar(a)=3bar(i)-2bar(j)+2bar(k)` and `bar(b)=-bar(i)-2bar(k)`
are the adjacent sides of a parallelogram. The angle between its diagonals is …………….

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The correct Answer is:
`:.theta=(pi)/(4)` OR `45^(@)`.
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bar(a)=2bar(i)-3bar(j)+2bar(k) and bar(b)=2bar(i)+3bar(j)+bar(k) are the sides of triangle OAB. Then its area is …… seq. unit.

If bar(a) = 3 bar(i) + 4 bar(j) + bar(k) and bar(b) = bar(i) + bar(j) - bar(k) , then "Comp"_(bar(b))bar(a)= . . . .

For unit vectors bar(a) and bar(b) , if bar(a)+2bar(b) and 5bar(a)-4bar(b) are perpendicular to each other then the angle between bar(a) and bar(b) is ………….

If bar(a) and bar(b) are adjacent sides of a rhombus, then bar(a).bar(b)=0 .

The vectors lambda bar(i)+bar(j)+2bar(k),bar(i)+lambda bar(j)-bar(k) and 2bar(i)-bar(j)+lambda bar(k) are coplanar, if …………

The value of lambda for which the vectors 3bar(i)-6bar(j)+bar(k) and 2bar(i)-4bar(j)+lambda bar(k) are parallel is …..

The vectors from origin to the points A and B are bar(a)=2bar(i)-3bar(j)+2bar(k) and bar(b)=2bar(i)+3bar(j)+bar(k) respectively, then the area of DeltaOAB is equal to …….

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

If bar(a)=bar(i)+bar(j)+bar(k) and bar(b)=bar(j)-bar(k) , then find a vector vec( c ) such that bar(a)xx bar( c )=bar(b) and bar(a).bar( c )=3 .

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

KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Objective type Questions)
  1. The angle between two vectors a and b with magnitudes sqrt(3) and 4, r...

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  2. Find the value of lambda such that the vectors bar(a)=2bar(i)+lambda b...

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  3. The value of lambda for which the vectors 3bar(i)-6bar(j)+bar(k) and 2...

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  4. The vectors from origin to the points A and B are bar(a)=2bar(i)-3bar(...

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  5. bar(a)=2bar(i)-3bar(j)+2bar(k) and bar(b)=2bar(i)+3bar(j)+bar(k) are t...

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  6. For any vector bar(a), the value of (bar(a)xx i)^(2)+(bar(a)xx j)^(2)+...

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  7. If |bar(a)|=10,|bar(b)|=2 and bar(a).bar(b)=12 then the value of |bar(...

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  8. The vectors lambda bar(i)+bar(j)+2bar(k),bar(i)+lambda bar(j)-bar(k) a...

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  9. If bar(a),bar(b) and bar( c ) are unit vectors such that bar(a)+bar(b)...

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  10. The projection vector of bar(a) on bar(b) is ………….

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  11. If bar(a),bar(b) and bar( c ) are three vectors such that bar(a)+bar(b...

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  12. If |bar(a)|=4 and -3le lambda le 2, then the range of |lambda. bar(a)|...

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  13. The number of vectors of unit length perpendicular to the vectors bar(...

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  14. The vector (bar(a)+bar(b)) bisects the angle between the non-collinear...

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  15. If bar( r ).bar(a)=0,bar( r ).bar(b)=0 and bar( r ).bar( c )=0 for som...

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  16. The vectors bar(a)=3bar(i)-2bar(j)+2bar(k) and bar(b)=-bar(i)-2bar(k) ...

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  17. The values of k, for which |k.bar(a)|lt |bar(a)| and k.bar(a)+(1)/(2)b...

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  18. The value of the expression |bar(a)xx bar(b)|^(2)+(bar(a).bar(b))^(2) ...

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  19. If |bar(a)xx bar(b)|^(2)+|bar(a).bar(b)|^(2)=144 and |bar(a)|=4, then ...

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  20. If bar(a) is any non-zero vector, then (bar(a).bar(i)).bar(i)+(bar(a...

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