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Find the vector equation of the plane pa...

Find the vector equation of the plane passing through the point `hati + hatj -2hatk` and `hati + 2hatj + hatk, 2hati - hatj + hatk.`

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`barr*(9hati + 3hatj -hatk)=14,9x+3y-z = 14`
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Find the vector equation of the plane passing through three points with position vectors hati + hatj - 2 hatk, 2 hati - hatj + hatk and hati + 2 hatj + hatk . Also find the co-ordinates of the point of intersection of this plane and the line vec(r) = 3 hati - hatj - hatk + lambda (2 hati - 2 hatj + hatk) .

The vector equation of the plane passing through the points hati+hatj-2hatk,2hati-hatj+hatk and hati+hatj+hatk , is

Find the vector equation of the plane passing through the point (3hati+4hatj+2hatk) and parallel to the vectors (hati+2hatj+3hatk) and (hati-hatj+hatk) .

Find the vector equation of the line passing through the point 2 hati + hatj - 3 hatk and perpendicular to the vectors hati + hatj + hatk and hati + 2 hatj - hatk .

(i) Find the equations of the plane passing through (a,b,c) and parallel to the plane vec(r) . (hati + hatj + hatk) = 2 . (ii) Find the vector equation of the plane through the point hati + hatj + hatk and parallel to the plane vec(r). (2 hati - hatj + 2 hatk) = 5 .

The vector equation of a line passing through the point hati + 2hatj + 3hatk and perpendicular to the vectors hati +hatj + hatk and 2hati - hatj + hatk is

Find the vector equation of the plane passing through the intersection of the planes vecr.(2hati+2hatj-3hatk)=7, vecr.(2hati+5hatj+3hatk)=9 and the point (2,1,3) .

Find the equation of the plane passing through the point hati-hatj+hatk and perpendicular to the vectro 3hati-hatj-2hatk and show that the point 2hati+4hatj lies on the plane.

NAVNEET PUBLICATION - MAHARASHTRA BOARD-PLANE -Example for Practice
  1. Find the vector and cartesian equation of the plane passing through th...

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  2. Find the vector equation of the plane passing through the point A(1, 0...

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  3. Find the vector equation of the plane passing through the point hati +...

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  4. Line barr = (hati - hatj + hatk) + lambda(2hati- hatj + hatk) containe...

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  5. Find the equations of the planes parallel to the plane x - 2y + 2z -4 ...

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  6. If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Z...

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  7. Find the cartesian form of the equation of the plane. barr = (hati ...

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  8. Find the vector equation of the plane passing through the intersection...

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  9. Find the equation of the plane passing through the intersection of the...

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  10. Prove that the lines (x-2)/1=(y-4)/4=(z-6)/7 and (x+1)/3=(y+3)/5=(z+5)...

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  11. A variable plane which remains at a constant distance 3p from the orig...

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  12. Find the angle between the planes whose vector equations are barr ...

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  13. If the line barr = (hati - 2hatj + 3hatk) + lambda(2hati + hatj + 2hat...

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  14. The planes barr *(3hati - 2hatj + phatk) =1 and barr *(-2hati + phatj ...

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  15. Find the value of p, if the planes barr *(phati - hatj + 2hatk) + 3 = ...

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  16. Find the angle between the line barr = (hati + 2hatj + hatk) + lambda(...

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  17. Find the angle between the line (x+1)/2=y/3=(z-3)/6and the plane 10 ...

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  18. Find the distance of the point 2hati + hatj + hatk) from the plane bar...

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  19. Find the distance of the point (1, 2-1) from the plane x -2y + 4z - 10...

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  20. Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the...

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