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Let A(1,1,1),B(23,5)a n dC(-1,0,2) be th...

Let `A(1,1,1),B(23,5)a n dC(-1,0,2)` be three points, then equation of a plane parallel to the plane `A B C` which is at distance is a. `2x-3y+z+2sqrt(14)=0` b. `2x-3y+z-sqrt(14)=0` c. `2x-3y+z+2=0` d. `2x-3y+z-2=0`

A

`2x-3y+z+2sqrt14=0`

B

`2x-3y+z-2sqrt14=0`

C

`2x-3y+z+2=0`

D

`2x-3y+z-2=0`

Text Solution

Verified by Experts

The correct Answer is:
a
A (1,1,1), B(2,3,5), C(-1,0,2) direction ratios of AB are `lt1,2,4gt`.
Direction ratios of AC are `lt-2,-1,1gt`. Therefore, direction ratios of normal to plane ABC are `lt-2,-3,1gt`
As a result, equation of the required plane be `2x-3y+z=0`.
Let the equation of the requried plane is `2x-3y+z=k`. Then
`|(k)/(sqrt(4+9+1))|=2ork=pm2sqrt14`
Hence, equation of the required plane is `2x-3y+z+2sqrt14=0`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  2. Let A( vec a)a n dB( vec b) be points on two skew lines vec r= vec a+...

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  3. Let A(1,1,1),B(23,5)a n dC(-1,0,2) be three points, then equation of a...

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  4. The point on the line (x-2)/1=(y+3)/(-2)=(z+5)/(-2) at a distance of 6...

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  8. The number of planes that are equidistant from four non-coplanar po...

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  9. In a three-dimensional coordinate system, P ,Q ,a n dR are images o...

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  12. Find the point of intersection of line passing through (0,0,1) and t...

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

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

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

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

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

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

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

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