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From the point P(a ,b ,c), let perpendic...

From the point `P(a ,b ,c),` let perpendicualars `P La n dP M` be drawn to `Y O Za n dZ O X` planes, respectively. Then the equation of the plane `O L M` is a. `x/a+y/b+z/c=0` b. `x/a+y/b-z/c=0` c. `x/a-y/b-z/c=0` d. `x/a-y/b+z/c=0`

A

`(x)/(a)+(y)/(b)+(z)/(c)=0`

B

`(x)/(a)+(y)/(b)-(z)/(c)=0`

C

`(x)/(a)-(y)/(b)-(z)/(c)=0`

D

`(x)/(a)-(y)/(b)+(z)/(c)=0`

Text Solution

Verified by Experts

The correct Answer is:
b
Coordinates of L and M are (0,b,c) and (a,0,c), respectively. Therefore, the equation of the plane passing through (0,0,0), (0,b,c) and (a,0,c) is
`|[x-0,y-0,z-0],[0,b,c],[a,0,c]|=0or(x)/(a)+(y)/(b)-(z)/(c)=0`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  4. The plane vecr cdot vecn = q will cotain the line vecr = veca + lambda...

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

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

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

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  8. The equation of the plane which passes through the line of intersec...

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

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

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

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  12. The ratio in which the line segment joining the points whose position...

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

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

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  15. L(1)andL(2) are two lines whose vector equations are L(1):vecr=lamda...

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

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

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  18. The line through of the plane passing through the lines (x-4)/(1)=(y-3...

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  19. The three planes 4y+6z=5,2x+3y+5z=5a n d6x+5y+9z=10 a. meet in a poi...

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  20. The equation of the plane through the line of intersection of the plan...

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