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Observe the following statements : Ass...

Observe the following statements :
Assertion (A) : Three vectors are coplanar if one of them is expressible as a linear combination of the other two.
Reason (R) : Any three coplanar vectors are linearly dependent.
Then which of the following is true?

A

Both A and R are true and R is the correct explanation of A.

B

Both A and R are true but R is not the correct explanation of A.

C

A is true, but R is false.

D

A is false, but R is true.

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - II
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  2. Statement-I : If two vectors are collinear then those vectors are copl...

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  3. Statement-I : Two non zero, non collinear vectors are linearly indepen...

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  4. The descending order of magnitudes of the vectors A=(i-j)/sqrt(2), B=b...

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  5. If D, E, F are mid points of sides BC, CA, AB of triangle ABC and G is...

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  6. Observe the following statements : Assertion (A) : Three vectors are...

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  7. If the vector bar(a)=2bar(i)+3bar(j)+6bar(k) and bar(b) are collinear ...

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  8. If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) ...

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  9. If the points whose position vectors are 2bar(i)+bar(j)+bar(k), 6bar(i...

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  10. Let bar(b)=bar(i)-2bar(j)+3bar(k), bar(a)=2bar(i)+3bar(j)-bar(k) and b...

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  11. The points whose position vectors are 2bar(i)+3bar(j)+4bar(k), 3bar(i)...

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  12. If bar(i)-2bar(j), 3bar(j)+bar(k), lambdabar(i)+3bar(j) are coplanar t...

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  13. If 3bar(i)+3bar(j)+sqrt(3)bar(k), bar(i)+bar(k), sqrt(3)bar(i)+sqrt(3)...

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  14. If bar(a)=bar(i)+4bar(j), bar(b)=2bar(i)-3bar(j) and bar(c)=5bar(i)+9b...

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  15. If bar(a), bar(b)&bar(c) are non-coplanar vectors and if bar(d) is suc...

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  16. Three non-zero non-collinear vectors bar(a), bar(b), bar(c) are such t...

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  17. The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+ba...

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  18. For three vectors bar(p), bar(q) and bar(r)" if "bar(r)=3bar(p)+4bar(q...

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  19. ABCDEF is a regualar hexagon whose centre is O. Then bar(AB)+bar(AC)+b...

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  20. P, Q, R and S are four points with the position vectors 3bar(i)-4bar(j...

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