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The Cartesian equation of the plane vecr...

The Cartesian equation of the plane `vecr=(1+lamda-mu)hati+(2-lamda)hatj+(3-2lamda+2mu)hatk` is a. `2x+y=5` b.`2x-y=5` c.`2x+z=5` d.`2x-z=5`

A

`2x+y=5`

B

`2x-y=5`

C

`2x+z=5`

D

`2x-z=5`

Text Solution

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The correct Answer is:
C
NA
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The Cartesian equation of the plane vecr=(1+lambda-mu)hati+(2-lambda)hatj+(3-2lambda+2mu)hatk is

The Cartesian equation of the plane vec r=(1+lambda-mu) hat i+(2-lambda) hat j+(3-2lambda+2mu) hat k is a. 2x+y=5 b. 2x-y=5 c. 2x+z=5 d. 2x-z=5

Find the Cartesian equation of the following plane: vecr=(lamda-2mu)hati+(3-mu)hatj+(2lamda+mu)hatk .

The equation of the plane containing the line vecr=hati+hatj+lamda(2hati+hatj+4hatk) is

Statement 1: Lthe cartesian equation of the plane vecr=(hati-hatj)+lamda(hati+hatj+hatk)+mu(hati-2hatj+3hatk) is 5x-2y-3z=7 Statement 2: The non parametric form of the plane vecr=veca+lamdavecb+muvecc is [(vecr,vecb,vecc)]=[(veca,vecb,vecc)]

Find the shortest distance between the two lines whose vector equations are given by: vecr=(1-lamda)hati+(-2lamda -2)hatj+(3-2lamda)hatk and vecr=(1+mu)hati+(2mu-1)hatj-(1+2mu)hatk

Find the shortest distance between the two lines whose vector equations are given by: vecr=(1+lamda)hati+(2-lamda)hatj+(-1+lamda)hatk and vecr=2(1+mu)hati-(1-mu)hatj+(-1+2mu)hatk

The projection of hati+hatj+hatk on the whole equation is vecr=(3+lamda)hati+(2lamda-1)hatj+3lamda hatk, lamda being the scalar parameter is:

Find the shortest distance between the lines gives by vecr=(8+3lamda)hati-(9+16lamda)hatj+(10+7lamda)hatk and vecr=15hati+29hatj+5hatk+mu(3hati+8hatj-5hatk) .

Find the vector equation of the plane vecr = 2 hati + hatj - 3 hatk + lamda ( 2hatj +hatk) + mu(5 hati + 2 hatj + hatk) in scalar product form.

OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Exercise
  1. Find the equation of plane passing through the line of intersection of...

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  2. Find the vector equation of the plane in which the lines vecr=hati+ha...

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  3. The Cartesian equation of the plane vecr=(1+lamda-mu)hati+(2-lamda)hat...

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  4. The perpendicular distance between the line vecr = 2hati-2hatj+3hatk+l...

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  5. The vector equation of the line of intersection of the planes vecr.(2h...

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  6. A straight line vecr=veca+lambda vecb meets the plane vecr. vec n=0 at...

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  7. The equation of the plane passing through three non - collinear points...

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  8. The length of the perpendicular from the origin to the plane passing t...

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  9. The equation of the plane containing the line (x-x1)/l=(y-y1)/m=(z-...

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  10. Find the shortest distance between the following pairs of lines whose ...

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  11. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2and (x-1)/(3k)=(y-1)/1=(z-6...

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  12. The direction ratios of a normal to the plane passing throuhg (0,0,1)...

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  13. A variable plane is at a distance, k from the origin and meets the coo...

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  14. Find the equation of the plane perpendicular to the line (x-1)/2=(y...

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  15. Find the equation of the plane through the points (2,2,1) and (9,3,6) ...

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  16. The equation of the plane containing the two lines (x-1)/2=(y+1)/(-1...

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  17. The direction ratios of the normal to the plane passing through the po...

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  18. The equation of a plane through the point (2, 3, 1) and (4, -5, 3) a...

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  19. The angle between the lines (x+4)/(1) = (y-3)/(2) = (z+2)/(3) and (x)/...

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  20. The equation of the plane which is perpendicular bisector of the line ...

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