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If a `hat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), and hat(i)+hat(j)+c hat(k)` are coplanar vectors, then what is the value of a+b+c-abc?

A

0

B

1

C

2

D

-2

Text Solution

Verified by Experts

The correct Answer is:
C
Vectors `vec(a)hat(i)+hat(j)+hat(k), hat(i) + b hat(j)+hat(k) and hat(i) + hat(j)+c hat(k)` are coplanar vectors.
`rArr |(a,1,1),(1,b,1),(1,1,c)|=0`
`rArr a(bc-1)-1(c-1)+1(1-b)=0`
`rArr abc-a-c+1+1-b=0`
`rArr a+b+c-abc=2`
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NDA PREVIOUS YEARS-VECTORS -MATH
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  2. Which one of the following statements is not correct?

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  4. For any three non-zero vectors veca,vecb and vec c if |(vecaxxvecb). v...

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  5. If vec(a)=vec(i)+2 hat(j)-3hat(k) and vec(b)=3hat(i)-hat(j)+lambda hat...

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  6. The vectors vec(AB)=vec(c), vec(BC)=vec(a), vec(CA)=vec(b), are the si...

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  7. If vec(a) is a position vector of a point (1, -3) and A is another poi...

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  8. If vec(a)=2hat(i)-3hat(j)-hat(k), vec(b)=hat(i)+4hat(j)-2hat(k), then ...

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  9. If -> a is a nonzero vector of magnitude a and lambda a nonzero...

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  10. Let vec(a) and vec(b) be the position vectors of A and B respectively....

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  11. Consider the following If vec(a) and vec(b) are the vectors forming ...

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  12. If vec(a) , vec(b), vec(c) are unit vectors such that vec(a) is perpen...

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  13. What is the locus of the point (x, y) for which the vectors (hat(i)-xh...

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  14. The number of vectors of unit length perpendicular to vectors vec ...

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  15. What is the area of the rectangle of which vec(r)=ahat(i)+b hat(j) is ...

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  16. If (3 vec(a)-vec(b))xx(vec(a) + 3 vec(b)) =k vec(a)xxvec(b) then what ...

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  17. What is the value of lambda if the triangle whose vertices are hat(i),...

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  18. The scalar triple product (vec(A)xxvec(B)).vec(C) of three vectors vec...

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  19. If vec a\ a n d\ vec b are unit vectors then write the value of | ve...

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  20. Two forces are equal to 2vec(OA) and 3vec(BO), their resultant being l...

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