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The area of the parallelogram having dia...

The area of the parallelogram having diagonals `vec(a)=3hat(i)+hat(j)-2hat(k) andvec(b)=hat(i)-3hat(j)+4k` is

A

4

B

`2sqrt(3)`

C

`4sqrt(3)`

D

`5sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
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The adjacent sides of a parallelogram are vec a = 3 hat i + lambda hat j + 4 hat k and vec b = hat i - lambda hat j + hat k (i) Find vec a xx vec b (ii) If the area of the paralleogram is sqrt 42 square units, find the value of lambda .

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SURA PUBLICATION-APPLICATIONS OF VECTORA ALGEBRA-ADDITIONAL QUESTIONS ( Choose the Correct or the most suitable answer from the given four alternatives : )
  1. If vec(d)=vec(a)xx(vec(b)xxvec(c))+vec(b)xx(vec(c)xxvec(a))+vec(c)xx(v...

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  2. If vec(a)andvec(b) are two unit vectors, then the vectors (vec(a)+vec(...

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  3. The area of the parallelogram having diagonals vec(a)=3hat(i)+hat(j)-2...

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  4. If vec(a),vec(b)andvec(c) are any three vectors, then vec(a)xx(vec(b)x...

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  5. The volume of the parallelepiped whose sides are given by bar(OA)=2hat...

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  6. If absvec(a)=absvec(b)=1" such that "vec(a)+2vec(b)and5vec(a)-4vec(b) ...

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  7. The angle between the vector 3hat(i)+4hat(j)+5hat(k) and the z-axis is

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  8. A vector vec(OP) makes 60^(@) and 45^(@) with the positive direction o...

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

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  10. If theta is the between the vector vec(a)andvec(b)," then " sintheta i...

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  11. If the vectors hat(i)+hat(j)+2hat(k),-hat(i)+2hat(k)and2hat(i)+xhat(j)...

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  12. If vec(a)=absvec(a)vec(e)" then "vec(e).vec(e) is

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  13. The value of |vec(a)+vec(b)|^(2)+|vec(a)-vec(b)|^(2) is

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  14. If vec(p)xxvec(q)=2hat(i)+3hat(j),vec(r)xxvec(s)=3hat(j)+2hat(k)," the...

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  15. If the work done by a force bar(F)=hat(i)+mhat(j)+hat(k) in moving the...

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  16. The two planes 3x + 3y - 3z - 1 = 0 and x + y - z + 5 = 0 are

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  17. The straight lines (x-3)/(2)=(y+5)/(4)=(z-1)/(-13)and(x+1)/(3)=(y-4)/(...

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  18. For what value of (vec(a)) will the straight lines (x+2)/(2)=(y)/(-3)=...

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  19. If [vec(a),vec(b),vec(c)]=3andabsvec(c)=1" then "|(vec(b)xxvec(c))xx(v...

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  20. If lambdahati+2lambdahatj+2lambdahatk is a unit vector,then the value ...

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