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Find the equation of a plane which passe...

Find the equation of a plane which passes through the point (3, 2, 0) and contains the line `(x-3)/1=(y-6)/5=(z-4)/4`

A

`x-y+z=1`

B

`x+y+z=5`

C

`x+2y-z=1`

D

`2x-y+z=5`

Text Solution

Verified by Experts

The correct Answer is:
a
The required plane is `|[x-3,y-6,z-4],[3-3,2-6,0-4],[1,5,4]|=0`
or `|[x-3,y-z-2,z-4],[0,0,-4],[1,1,4]|=0`
`("Operating"C_(2)toC_(2)-C_(3))`
or `4(x-3-y+z+2)=0`
or `x-y+z=1`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
  1. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

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  2. Two systems of rectangular axes have the same origin. If a plane cu...

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  3. Find the equation of a plane which passes through the point (3, 2, 0...

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  4. The direction ratios of a normal to the plane through (1,0,0)a n d(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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