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If the vectors hat(i)+hat(j)+2hat(k),-ha...

If the vectors `hat(i)+hat(j)+2hat(k),-hat(i)+2hat(k)`and`2hat(i)+xhat(j)-yhat(k)` are mutually orthogonal, then the values of x, y, z are

A

`(10,4,1)`

B

`(-10,4,1)`

C

`(-10,-4,(1)/(2))`

D

`(-10,4,(1)/(2))`

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Let alpha in R and the three vectors a=alpha hat(i) + hat(j) +3hat(k) , b=2hat(i) +hat(j) -alpha hat(k) " and " c= alpha hat(i) -2hat(j) +3hat(k) . Then the set S={alpha: a,b " and c are coplanar"}

SURA PUBLICATION-APPLICATIONS OF VECTORA ALGEBRA-ADDITIONAL QUESTIONS ( Choose the Correct or the most suitable answer from the given four alternatives : )
  1. The area of the parallelogram having diagonals vec(a)=3hat(i)+hat(j)-2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. For any three vectors vec(a),vec(b)andvec(c),(vec(a)+vec(b)).(vec(b)+v...

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  20. If the vector ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k)andhat(i)+ha...

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