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If bar(a)=bar(i)+bar(j), bar(b)=bar(j)+b...

If `bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k), bar(c)=bar(i)+bar(k)`, then the unit vector in the opposite direction of `bar(a)-2bar(b)+3bar(c)` is

A

`1/(3sqrt(2))(4bar(i)-bar(j)+bar(k))`

B

`-1/(3sqrt(2))(4bar(i)-bar(j)+bar(k))`

C

`1/(3sqrt(2))(bar(i)-4bar(j)+bar(k))`

D

`1/(3sqrt(2))(bar(i)+bar(j)-4bar(k))`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - I
  1. The position vectors of A and B are bar(a) and bar(b) respectively. If...

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  2. If lambda(2bar(i)-4bar(j)+4bar(k)) is a unit vector then lambda=

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  3. If bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k), bar(c)=bar(i)+bar(k), t...

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  4. The unit vector(s) parallel to bar(i)-3bar(j)-5bar(k) is

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  5. If bar(OP)=2bar(i)+3bar(j)-bar(k), bar(OQ)=3bar(i)-4bar(j)+2bar(k) the...

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  6. Unit vector making angles pi/6, pi/6, pi/3 with bar(i), bar(j), bar(k)...

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  7. If a straight line makes an angle cos^(-1)(1/sqrt(3)) with each of the...

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  8. If (bar(a), bar(b))=60^(@)" then "(-bar(a), -bar(b))=

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  9. Any two collinear vectors are

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  10. Any three coplanar vectors are

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  11. If bar(a) and bar(b) are two non-zero, non-collinear vectors such that...

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  12. If bar(a)=bar(i)-2bar(j)+bar(k), bar(b)=4bar(i)+2bar(j)-bar(k), bar(c)...

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  13. If bar(a)=bar(i)+2bar(j)+2bar(k) and bar(b)=3bar(i)+6bar(j)+2bar(k) th...

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  14. If 2bar(i)+3bar(j)-6bar(k), 6bar(i)-2bar(j)+3bar(k) are two consecutiv...

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  15. If ABCD is a parallelogram such that bar(AB)=bar(a), bar(BC)=bar(b)" t...

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  16. A point C = (5a + 4b - 5c)/(3) divides the line joining A = a - 2b + 3...

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  17. P, Q, R, S have position vectors bar(p), bar(q), bar(r), bar(s) respec...

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  18. The ratio in which the line segment joining the points with P.V.'s bar...

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  19. The ratio in which bar(i)+2bar(j)+3bar(k) divides the join of -2bar(i)...

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  20. Let 'O' be the origin and A, B be two points. bar(p), bar(q) are vecto...

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