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If lines x=y=za n dx=y/2=z/3 and third l...

If lines `x=y=za n dx=y/2=z/3` and third line passing through `(1,1,1)` form a triangle of area `sqrt(6)` units, then the point of intersection of third line with the second line will be a. `(1,2,3)` b. `2,4,6` c. `4/3,6/3,(12)/3` d. none of these

A

(1,2,3)

B

(2,4,6)

C

`((4)/(3),(8)/(3),(12)/(3))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
Let any point on the second line be `(lamda,2lamda,3lamda)`

`costheta=(6)/(sqrt42),sintheta=(sqrt6)/(sqrt42)`
`Delta_(OAB)=(1)/(2)(OA)OBsintheta`
`=(1)/(2)sqrt(3)lamdasqrt14xxsqrt(6)/sqrt(42)=sqrt(6)`
or `lamda=2`
So B is (2,4,6)
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  6. Distance of point P(vecP) from the plane vecr.vecn=0 is

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

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  8. The angle theta between the line vecr=veca+lambdavecb and the plane ve...

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

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  10. The ratio in which the plane vec rdot( vec i-2 vec j+3 vec k)=17 d...

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  13. Let L be the line of intersection of the planes 2x+3y+z=1a n dx+3y+2z=...

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

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

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

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

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

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