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Vector equation of the plane r=i-j+lambd...

Vector equation of the plane `r=i-j+lambda(i+j+k)+mu(i-2j+3k)` in the scalar dot product form is

A

`vecr.(5hati-2hatj-3hatk)=7`

B

`vecr.(5hati+2hatj+3hatk)=7`

C

`vecr.(5hati-2hatj-3hatk)=-7`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly given plane passes throughthe point `a=hati-hatj` and is parallel to the vectors `vecb=hati+hatj+hatk` and `vecc=hati-2hatj+3hatk`
So it is perpendicular to the vector `vecn` given by
`vecn=vecbxxvecc=|(hati,hatj,hatk),(1,1,1),(1,-2,3)|=5hati-2hatj-3hatk`
The vector equation of the plane in scalar product form is
`vecr.vecn=veca.vecn`
`impliesvecr.(5hati-2hatj-3hatk)=(hati-hatj).(5hati-2hatj-3hatk)`
`impliesvecr.(5hati-2hatj-3hatk)=7`
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OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Chapter Test
  1. Vector equation of the plane r=i-j+lambda(i+j+k)+mu(i-2j+3k) in the sc...

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

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  3. The value of lamda for which the lines (x-1)/1=(y-2)/(lamda)=(z+1)/(-1...

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

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  5. The direction cosines of the line 6x-2=3y+1=2z-2 are

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  6. A line passes through two points A(2,-3,-1) and B(8,-1,2). The coordin...

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  7. The position vector of a point at a distance of 3sqrt(11) units from h...

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  8. The line joining the points 6veca-4vecb+4vecc, -4vecc and the line joi...

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  9. The image (or reflection) of the point (1,2-1) in the plane vecr.(3hat...

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

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  11. Angle between the line vecr=(2hati-hatj+hatk)+lamda(-hati+hatj+hatk) a...

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  12. The line through hati+3hatj+2hatkandbot"to the line "vecr=(hati+2hatj-...

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  13. The distance of the point having position vector -hat(i) + 2hat(j) + 6...

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  14. The position vector of the point in which the line joining the points ...

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  15. The two lines vecr=veca+veclamda(vecbxxvecc) and vecr=vecb+mu(veccxxve...

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  16. Lines vecr = veca(1) + lambda vecb and vecr = veca(2) + svecb will lie...

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  17. Equation of a line passing through (-1,2,-3) and perpendicular to the ...

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  18. Find the Vector and Cartesian equation of line passing through (1, -2,...

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  19. The distance between the planes given by vecr.(hati+2hatj-2hatk)+5=0...

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  20. Find shortest distance between the line vecr = (5hati + 7hatj + 3ha...

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  21. Find the shortest distance between the lines vecr=(hatii+2hatj+hatk)+l...

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