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If A(2bar(i)-bar(j)-3bar(k)), B(4bar(i)+...

If `A(2bar(i)-bar(j)-3bar(k)), B(4bar(i)+bar(j)-bar(k)), C(bar(i)-3bar(j)+2bar(k)), D(bar(i)-bar(j)-2bar(k))` then the vector equation of the plane parallel to `bar(ABC)` and passing through the centroid of the tetra-hedron ABCD is

A

`bar(r)=(2bar(i)-bar(j)-bar(k))+s(bar(i)+bar(j)+bar(k))+t(bar(i)+2bar(j)-5bar(k))`

B

`bar(r)=(2bar(i)-bar(j)+bar(k))+s(bar(i)-bar(j)+bar(k))+t(bar(i)+2bar(j)+5bar(k))`

C

`bar(r)=(2bar(i)+bar(j)-bar(k))+s(bar(i)+bar(j)-bar(k))+t(bar(i)-2bar(j)+5bar(k))`

D

`bar(r)=(2bar(i)+bar(j)+bar(k))+s(bar(i)-bar(j)-bar(k))+t(bar(i)+2bar(j)-5bar(k))`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - I
  1. If bar(a)=bar(i)-2bar(j)+bar(k), bar(b)=4bar(i)+2bar(j)-bar(k), bar(c)...

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

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

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

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

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

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

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

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

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  10. The vector equation of the line passing through the point 2bar(i)+bar(...

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  11. The equation to the line passing through the points A(bar(i)+bar(j)+ba...

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  12. The cartesian equation of the line passing through the point (2, -1, 4...

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  13. The cartesian equation to the line passing through the points A(1, 2, ...

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  14. If bar(a), bar(b), bar(c) are three non-coplanar vectors, then the vec...

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  15. If bar(a), bar(b) are two non collinear vectors, then bar(r)=sbar(a)+t...

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  16. If bar(r)=sbar(a)+tbar(b) represents a line passing through the points...

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  17. If A(2bar(i)-bar(j)-3bar(k)), B(4bar(i)+bar(j)-bar(k)), C(bar(i)-3bar(...

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  18. The vector equation of the plane passing through the points (1, -2, 5)...

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  19. ABCD is a parallelogram and P is themid point of the side AD. The line...

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  20. The cartesian equation of the plane whose vector equation is bar(r)=...

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