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`bar(a) , bar(b), bar (c )`, are non-coplanar vectors, Prove that the following four points are coplanar.
`6bar(a) + 2bar(b) - bar(c ), 2bar(a) - bar(b) + 3bar(c ), -bar(a) + 2bar(b)-4bar(c ), -12bar(a)-bar(b)-3bar(c )`.

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`bar(AB), bar(AC) and bar (AD) ` are coplanar
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bar(a), bar(b), bar(c) are non-coplanar vectors. Prove thate the following four points are coplanar - bar(a) + 4 bar(b) - 3 bar(c) , 3 bar(a) + 2 bar(b) - 5 bar(c) - 3 bar(a) + 8 bar(b) - 5 bar(c) , - 3 bar(a) + 2 bar(b) + bar(c)

Show that the following vectors are linearly dependent bar(a)-2bar(b)+3bar(c), -2bar(a)+3bar(b)-4bar(c), -bar(b)+2bar(c)

If bar(a), bar(b), bar(c) are non coplanar vectors, then test for the collinearity of the following points whose position vectors are given. i) bar(a)-2bar(b)+3bar(c), 2bar(a)+3bar(b)-4bar(c), -7bar(b)+10bar(c) ii) 3bar(a)-4bar(b)+3bar(c), -4bar(a)+5bar(b)-6bar(c), 4bar(a)-7bar(b)+6bar(c) iii) 2bar(a)+5bar(b)-4bar(c), bar(a)+4bar(b)-3bar(c), 4bar(a)+7bar(b)-6bar(c)

Show that the following vectors are linearly dependent 3bar(a)-2bar(b)-4bar(c), -bar(a)+2bar(c), -2bar(a)+bar(b)+3bar(c)

Compute bar(a) xx (bar(b) + bar(c )) + bar(b) xx (bar(c ) +bar(a)) + bar(c ) xx (bar(a)+bar(b))

Prove that the following four points are coplanar. i) 4bar(i)+5bar(j)+bar(k), -bar(j)-bar(k), 3bar(i)+9bar(j)+4bar(k), -4bar(i)+4bar(j)+4bar(k) ii) -bar(a)+4bar(b)-3bar(c), 3bar(a)+2bar(b)-5bar(c), -3bar(a)+8bar(b)-5bar(c), -3bar(a)+2bar(b)+bar(c)" ("bar(a), bar(b), bar(c) are non-coplanar vectors) iii) 6bar(a)+2bar(b)-bar(c), 2bar(a)-bar(b)+3bar(c), -bar(a)+2bar(b)-4bar(c), -12bar(a)-bar(b)-3bar(c)" ("bar(a), bar(b), bar(c) are non-coplanar vectors)

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-ADDITION OF VECTORS -Exercise - 4 (a)
  1. If the vectors - 3 bar(i) + 4 bar(j) + lambda bar(k) and mu bar(i)+ 8...

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  2. ABCDE is a pentagon. If the sum of the vectors bar(AB),bar(AE), bar(...

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  3. If the position vectors of the points A,B,C are -2bar(i)+bar(j)-bar(...

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  4. If bar(OA) = bar(i) + bar(j)+ bar(k), bar(AB) = 3bar(i)-2bar(j)+bar(k)...

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  5. If bar(a) = 2bar(i)+5bar(j)+bar(k) and bar(b) = 4bar(i)+mbar(j)+nbar(k...

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  6. Let bar(a) = 2bar(i) +4bar(j)-5bar(k), bar(b) = bar(i)+bar(j)+bar(k), ...

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  7. If the triangle formed by the vectors 3 bar(i) + 5 bar(j) + 2 bar(k) ,...

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  8. If alpha, beta and gamma be the angle made by the vector 3bar(i)-6bar(...

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  9. Find the angles made by the straight line passing through the points (...

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

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  11. bar(a), bar(b), bar(c) are non-coplanar vectors. Prove thate the follo...

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  12. bar(a) , bar(b), bar (c ), are non-coplanar vectors, Prove that the fo...

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  13. If bar(i), bar(j), bar(k) are unit vectors along the positive directio...

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

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

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

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  17. In the cartesian plane, O is the origin of the coordinate axes. A pers...

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  18. The points O, A, B, X and Y are such that bar(OA)=bar(a), bar(OB)=bar(...

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  19. In DeltaOAB, E is the midpoint of AB and F is a point on OA such that ...

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  20. The point 'E' divides the segment PQ internally in the ratio 1 : 2 and...

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