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Let A(2,-1,4) and B(0,2,-3) be the point...

Let `A(2,-1,4)` and `B(0,2,-3)` be the points and C be a point on AB produced such that `2AC=3AB`, then the coordinates of C are

A

`(1/2,5/4,-5/4)`

B

`(-1/2,7/4,-13/4)`

C

`(6,-7,18)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have
`2AC=3AB`

`implies2AC=3(AC-BC)impliesAC=3BCimplies(AC)/(BC)=3/1`
`impliesC` divides AB externally in the ratio `3:1`.
`:.` Coordinates of C are
`((3xx0-2xx1)/(3-1),(3xx2-xx-1)/(3-1),(3xx(-3)-1xx4)/(3-1))` or `(-1,7/2,(-13)/2)`
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OBJECTIVE RD SHARMA-THREE DIMENSIONAL COORDINATE SYSTEM -Exercise
  1. Let A(2,-1,4) and B(0,2,-3) be the points and C be a point on AB produ...

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  2. If the x-coordinate of a point P on the join of Q(2,2,1) and R(5,1,-2)...

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  3. The distance of the point P(a,b,c) from the x-axis is

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  4. Ratio in which the xy-plane divides the joint of (1,2,3) and (4,2,1), ...

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  5. If P(3,2,-4),Q(5,4,-6) and R(9,8,-10) are collinear, then R divides PQ...

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  6. A(3,2,0),B(5,3,2),(-9,6,-3) are the vertices of /\ ABC and AD is the b...

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  7. A line passes through the points (6,-7,-1)a n d(2,-3,1)dot Find te ...

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  8. If a line makes angles alpha,beta,gamma with the positive direction of...

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  9. If P is a point in space such that OP=12 and vec(OP) is inclied at ang...

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  10. A vector vec O P is inclined to O Xa t45^0a n dO Ya t60^0 . Find the ...

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  11. A vector vecr is equally inclined with the coordinates axes. If the ti...

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  12. If vecr is a vector of magnitude 21 and has direction ratios proporti...

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  13. The direction cosines of the lines bisecting the angle between the lin...

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  14. Find the coordinates of the foot of the perpendicular drawn from po...

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  15. The foot of the perpendicular drawn from a point with position vector ...

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  16. The projections of a directed line segment on the coordinate axes are ...

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  17. Let l1,m1,n1; l2,m2,n2 and l3,m3,n3 be the direction cosines of three ...

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  18. If P(x ,y ,z) is a point on the line segment joining Q(2,2,4)a n d ...

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  19. If O is the origin, O P=3 with direction ratios -1,2,a n d-2, then fin...

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  20. A mirror and a source of light are situated at the origin O and at ...

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  21. Find the angel between any two diagonals of a cube.

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