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A set of vectors bar(a)(1), bar(a)(2), …...

A set of vectors `bar(a)_(1), bar(a)_(2), ………, bar(a)_(n)` is said to linearly independent if every relation of the form `l_(1)bar(a)_(1)+l_(2)bar(a)_(2)+……….+l_(n)bar(a)_(n)=bar(0)` implies

A

`l_(1)=l_(2)=…………..=l_(n)=1`

B

`l_(1)=l_(2)=……………=l_(n)=0`

C

`l_(1)=l_(2)=…………=l_(n)`

D

`l_(1)+l_(2)+…………..+l_(n)=0`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-PROPERTIES OF VECTORS-PRACTICE EXERCISES
  1. If the position vectors of the four points A, B, C, D are 2bar(a), bar...

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  2. If the position vectors of three consecutive vertices of a parallelogr...

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  3. A set of vectors bar(a)(1), bar(a)(2), ………, bar(a)(n) is said to linea...

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  4. If 4bar(i)+7bar(j)+8bar(k), 2bar(i)+3bar(j)+4bar(k), 2bar(i)+5bar(j)+7...

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  5. If A=(1, 1, 1), B=(1, 2, 3), C=(2, -1, 1) be the vertices of a DeltaAB...

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  6. If A is the point bar(a)+2bar(b), P is the point bar(a) and P devides ...

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  7. The ratio in which 3bar(i)+4bar(j)+7bar(k) divides the join of bar(i)+...

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  8. In a DeltaOAB, E is the mid point of OB and D is a point in AB such th...

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  9. If 2bar(i)+3bar(j)+5bar(k), 2bar(i)+4bar(j)+5bar(k) and 2bar(i)+4bar(j...

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  10. The P.V.'s of A, B, C are bar(i)+bar(j)+bar(k), 4bar(i)+bar(j)+bar(k),...

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  11. In a DeltaABC, P.V.'s of A, mid-point of BC are bar(i)+2bar(j)+3bar(k)...

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  12. If G is the centroid of DeltaABC then bar(GA)+bar(GB)+bar(GC)=

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  13. If G is the centroid of Delta ABC, G' is the centroid of Delta A' B' C...

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  14. If D, E are the midpoints of AB, AC of Delta ABC, then vec(B)E + vec(D...

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  15. If D is the midpoint of the side BC of a triangle ABC then bar(AB)^(2)...

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  16. Find the area of the parallelogram whose adjacent sides are bar(a) = 2...

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  17. If the diagonals of a parallelogram are bar(i)+5bar(j)-2bar(k) and -2b...

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  18. Let bar(a), bar(b), bar(c), bar(d) be the position vectors of A, B, C ...

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  19. If bar(a), bar(b) represent bar(AB), bar(BC) respectively of a regular...

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  20. When a right handed rectangular cartesian system oxyz is rotated about...

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