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The centre of the circle given by vecr.(...

The centre of the circle given by `vecr.(hati+2hatj+2hatk)=15and|vecr-(hatj+2hatk)=4` is

A

(0,1,2)

B

(1,3,4)

C

(-1,3,4)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
The equation of the line through the center `hatj+2hatj` and normal to the given plane is
`vecr=hatj=2hatk+lamda(hati+2hatj+2hatk)" "(i)`
This meets the plane for which
`[hatj+2hatk+lamda(hati+2hatj+2hatk)].(hati+2hatj+2hatk)=15`
or `6+9lamda=15orlamda=1`
Putting in (i), we get
`vecr=hatj+2hatk+(hati+2hatj+2hatk)=hati+3hatj+4hatk`
Hence, centre is (1,3,4).
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  2. The direction ratios of a normal to the plane through (1,0,0)a n d(...

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  3. The centre of the circle given by vecr.(hati+2hatj+2hatk)=15and|vecr-(...

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  4. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c ...

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  5. Distance of the point P(vecc) from the line vecr=veca+lamdavecb is

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  6. From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to...

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  7. The plane vecr cdot vecn = q will cotain the line vecr = veca + lambda...

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  8. The projection of point P(vecp) on the plane vecr.vecn=q is (vecs), th...

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  9. The angle between hati and line of the intersection of the plane vecr...

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  10. The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles ...

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  11. The equation of the plane which passes through the line of intersect...

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  12. Consider triangle A O B in the x-y plane, where A-=(1,0,0),B-=(0,2,0)a...

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  13. Let veca=hati+hatj and vecb=2hati-hatk. Then the point of intersection...

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  14. The co-ordinates of the point P on the line vecr =(hati +hatj + hatk...

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  15. The ratio in which the line segment joining the points whose positi...

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  16. Which of the following are equation for the plane passing through the ...

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  17. Given vecalpha=3 hat i+ hat j+2 hat ka n d vecbeta= hat i-2 hat j-4 h...

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  18. L1a n dL2 and two lines whose vector equations are L1: vec r=lambda((c...

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  19. The shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/1a ...

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  20. The line through hati+3hatj+2hatk and perpendicular to the lines vecr=...

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