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Show that the following vectors are line...

Show that the following vectors are linearly dependent
i) `bar(i)+bar(j)+2bar(k), bar(j)+2bar(k), bar(i)+2bar(j)+4bar(k)`

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Show that the following vectors are linearly dependent bar(i)+bar(j), bar(j)+bar(k), -bar(k)+bar(i)

Find the value of [bar(i)+bar(j)+bar(k),bar(i)-bar(j),bar(i)+2bar(j)-bar(k)] .

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

Compute [bar(i) - bar(j). bar(j) - bar(k). bar(k) -bar(i)] .

Show that the triangle formed by the vectors 3bar(i)+5bar(j)+2bar(k), 2bar(i)-3bar(j)-5bar(k), -5bar(i)-2bar(j)+3bar(k) is equilateral.

If the position vectors of the points A,B,C are -2bar(i)+bar(j)-bar(k), -4bar(i)+2bar(j)+2bar(k), 6bar(i)-3bar(j)-13bar(k) respectively and bar(AB) = lambda bar(AC) then find the value of lambda .

Find the volume of the tetrahedron having the edges , bar(i) + bar(j) + bar(k), bar(i)-bar(j), bar(i) + 2bar(j) + bar(k) .

Find unit vector perpendicular to both bar(i) + bar(j) + bar(k) and 2bar(i) + bar(j) + 3bar(k) .

Write the position vector of the centroid of the triangle formed by the points whose position vectors are 3bar(i)+2bar(j)-bar(k), 2bar(i)-2bar(j)+5bar(k), bar(i)+3bar(j)-bar(k) .

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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