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Shortest distance between the lines `(x-1)/1=(y-1)/1=(z-1)/1a n d(x-2)/1=(y-3)/1=(z-4)/1` is equal to

A

`sqrt14`

B

`sqrt7`

C

`sqrt2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
c
The given lines are parallel.

From the figure, we get
`BC=((2-1)1)/(sqrt3)+((3-1)1)/(sqrt3)+((4-4)1)/(sqrt3)`
`=(1+2+3)/(sqrt3)=2sqrt3`
`AB=sqrt(1+4+9)=sqrt14`
Shortest distance `=AB=sqrt(14-12)=sqrt(2)`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  2. Find the point of intersection of line passing through (0,0,1) and ...

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  3. Shortest distance between the lines (x-1)/1=(y-1)/1=(z-1)/1a n d(x-2...

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  4. Distance of point P(vecP) from the plane vecr.vecn=0 is

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  5. The reflection of the point veca in the plane vecr.vecn=q is (A) veca+...

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  6. The line vecr= veca + lambda vecb will not meet the plane vecr cdot ...

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  7. If a line makes an angel of pi/4 with the positive direction of eac...

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  8. The ratio in which the plane vecr.(veci-2 vecj+3veck)=17 divides the l...

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  9. then image of the point (-1,3,4) in the plane x-2y=0

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  10. The perpendicular distance between the line vecr = 2hati-2hatj+3hatk+l...

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  11. Let L be the line of intersection of the planes 2x""+""3y""+""z""="...

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  12. The length of the perpendicular drawn from (1,2,3) to the line (x-6...

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  13. If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the pl...

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  14. The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2=...

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  15. If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordi...

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  16. A line makes an angel theta with each of the x-and z-axes. If the a...

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  17. The shortest distance from the plane 12 x+y+3z=327to the sphere x^2+y^...

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  18. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

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  19. The radius of the circle in which the sphere x^(I2)+y^2+z^2+2z-2y-4z...

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  20. The lines (x-2)/1=(y-3)/2=(z-4)/(-k)a n d=(x-1)/k=(y-4)/2=(z-5)/1 are ...

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