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Find the shortest distance between the lines `(x-1)/2=(y-2)/3=(z-3)/4a n d(x-2)/3=(y-4)/4=(z-5)/5` .

A

`x-2y+z=0`

B

`x-2y+z+7=0`

C

`x+y+z=0`

D

`x+y+z=9`

Text Solution

Verified by Experts

The correct Answer is:
A
We have both the lines are coplanar, hence the equation of their plane is
`|{:(x-x_(1),y-y_(1),z-z_(1)),(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)):}|=0`
`:." "|{:(x-1,y-2,z-3),(2,3,4),(3,4,5):}|=0`
`:.-(x-1)+2(y-2)-(z-3)=0`
`rArr" "(x-1)-2(y-2)+z-3)=0`
`:." "x-2y+z=0`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PLANE-Practice exercise (Exercise 1) Topical problems (Coplanarity of two lines and distance of a point from a plane)
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  2. The distance of a plane Ax+By+Cz=D from the point (x(1),y(1),z(1)) is

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  3. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha,...

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  4. If the foot of the perpendicular from O(0,0,0) to a plane is P(1,2,2)....

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  5. If (2,-1,3) is the foot of the perpendicular down from the origin to t...

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  6. let Q be the foot of perpendicular from the origin to the plane 4x-3y+...

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  7. The distance of the point (1,-5,9) from the plane x-y+z = 5 measured a...

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  8. If the straight lines x 1 y 1 z 2 k 2 and x 1 y 1 z 5 2 k are copl...

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  9. If the straighat lines x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=...

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  10. Show that the lines (x+1)/-3=(y-3)/2=(z+2)/1 and x/1=(y-7)/-3=(z+7)/2 ...

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  11. If the lines (x+1)/(2)=(y-1)/(1)=(z+1)/(3)and(x+2)/(2)=(y-k)/(3)=(z)/(...

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  12. Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/...

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  13. Find the equation of a plane which passes through the point (3, 2, ...

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  14. If the lines (x-2)/1=(y-3)/1)(z-4)/(-k) and (x-1)/k=(y-4)/2=(z-5)/1 ar...

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  15. The coordinate of the foot of perpendicular drawn from origin to a pla...

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  16. Let a plane passes through the point P(-1,-1,1) and also passes throug...

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