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i) bar(a), bar(b), bar(c) are pairwise n...

i) `bar(a), bar(b), bar(c)` are pairwise non zero and non collinear vectors. If `bar(a)+bar(b)` is collinear with `bar(c) and bar(b)+bar(c)` is collinear with `bar(a)` then find the vector `bar(a)+bar(b)+bar(c)`.
ii) If `bar(a)+bar(b)+bar(c)=alphabar(d), bar(b)+bar(c)+bar(d)=betabar(a) and bar(a), bar(b), bar(c)` are non coplanar vectors, then show that `bar(a)+bar(b)+bar(c)+bar(d)=bar(0)`.

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The correct Answer is:
i) `bar(0)`
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bar(a), bar(b) , bar(c ) are pair wise non zero and non collinear vectors. If bar(a) + bar(b) is collinear with bar(c ) and bar(b) + bar(c ) is collinear with bar(a) then find vector bar(a) + bar(b) + bar(c ) .

bar(a), bar(b), bar(c) are non-zero vectors and no two of them are collinear. If bar(a)+2bar(b) is collinear with bar(c) and bar(b)+3bar(c) is collinear with bar(a) . Then find bar(a)+2bar(b)+6bar(c) .

Find a linear relation between the vectors bar(a)+3bar(b)+4bar(c), bar(a)-2bar(b)+3bar(c), bar(a)+5bar(b)-2bar(c) and 6bar(a)+14bar(b)+4bar(c)" where "bar(a), bar(b), bar(c) are non coplanar vectors.

Show that the points whose P,V are -2bar(a)+3bar(b)+5bar(c ), bar(a)+2bar(b)+3bar(c ) , 7bar(a)-bar(c ) are collinear, where bar(a),bar(b), bar(c ) are non-coplanar vectors.

Show that the following vectors are linearly dependent bar(a)-2bar(b)+bar(c), 2bar(a)+bar(b)-bar(c), 7bar(a)-4bar(b)+bar(c) where bar(a), bar(b), bar(c) are non-coplanar vectors

AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - 1.1 SHORT ANSWER QUESTIONS
  1. ABCDE is a pentagon. If the sum of the vectors bar(AB),bar(AE), bar(...

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  2. If ABCDEF is a regular hexagon with centre O , then P.T bar(AB)+bar(A...

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  3. If bar(a), bar(b), bar(c) are non coplanar vectors, then test for the ...

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  4. Show that the points whose P,V are -2bar(a)+3bar(b)+5bar(c ), bar(a)+2...

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  5. i) bar(a), bar(b), bar(c) are pairwise non zero and non collinear vect...

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  6. i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that...

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  7. Prove that the following four points are coplanar. i) 4bar(i)+5bar(j...

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  8. If the points whose position vectors are 3bar(i) -2bar(j)-bar(k), 2bar...

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  9. Show that the following vectors are linearly dependent i) bar(i)+bar...

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  10. Show that the following vectors are linearly dependent bar(i)+bar(j)...

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  11. Show that the following vectors are linearly dependent bar(a)-2bar(b...

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  12. Show that the following vectors are linearly dependent bar(a)-2bar(b...

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  13. Show that the following vectors are linearly dependent 3bar(a)-2bar(...

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  14. If the vectors bar(a)=bar(i)+bar(j)+bar(k), bar(b)=4bar(i)+3bar(j)+4ba...

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  15. If bar(a), bar(b), bar(c) are linearly independent vectors, then show ...

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  16. Find a linear relation between the vectors bar(a)+3bar(b)+4bar(c), bar...

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