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Find the vector equation of a plane whic...

Find the vector equation of a plane which is at a distance of 6 units from the origin and which is normal to the vector `(hati+2hatj-2hatk)`.

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Here, `vecn=(hati+2hatj-2hatk)` and p=6.
`therefore hatn=(hati+2hatj-2hatk)/sqrt(1^(2)+2^(2)+(-2)^(2))=(1/3hati+2/3hatj-2/3hatk)`.
So, the vector equation of the plane is
`vecr.hatn=p rArr vecr.(1/3hati+2/3hatj-2/3hatk)=6`.
`rArr vecr=(hati+2hatj-2hatk)=18`.
Hence, the required vector equation of the plane is
`vecr.(hati+2hatj-2hatk)=18`.
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RS AGGARWAL-THE PLANE-Objective Questions
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  3. The direction cosines of the normal to the plane 5y+4=0 are

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  4. The length of perpendicular from the origin to the plane vecr.(-3hati-...

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  6. A plane cuts off intercepts 3,-4,6 on the coordinate axes. The length ...

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  7. If the line (x+1)/3=(y-2)/4=(z+6)/5 is parallel to the planes 2x-3y+kz...

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  8. यदि O मूल बिंदु तथा P के निर्देशांक (1 ,2 ,-3 ) है तो बिंदु P से जा...

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  9. The line (x-4)/1=(y-2)/1=(z-k)/2 lies exactly on the plane 2x=4y+z=7 t...

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  10. The plane 2x+3y+4z=12 meets the coordinate axes in A,B and C. The cent...

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  11. If a plane meets the coordinate axes in A,B and C such that the centro...

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  12. The equation of a plane through the point A(1,0,-1) and perpendicular ...

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  13. The line (x-1)/2=(y-2)/3=(z-3)/4 meets the plane 2x+3y-z=14 in the poi...

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

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  15. Find the equation of the plane through the intersection of the planes ...

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  16. The equation of the plane passing through the points A(0,-1,0), B(2,1,...

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  17. If the plane 2x-y+z=0 is parallel to the line (2x-1)/2=(2-y)/2=(z+1)/a...

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  18. The angle between the line (x+1)/1=y/2=(z-1)/1 and a normal to the pla...

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  19. The point of intersection of the line (x-1)/3=(y+2)/4=(z-3)/-2 and the...

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  20. The equation of a plane passing throgh the points A(a,0,0), B(0,b,0) a...

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  21. If theta is the angle between the planes 2x-y+2z=3 and 6x-2y+3z=5, the...

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