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Prove tht the normals to the planes 4x+1...

Prove tht the normals to the planes `4x+11y+2z+3=0` and `3x-2y+5z=8` are perpendicular to each other.

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`vecn_(1)=(4hati+11hatj+2hatk)` and `vecn_(2)=(3hati-2hatj+5hatk)`.
`therefore vecn_(1).vecn_(2)=(4 xx 3) + 11xx (-2) + 2 xx 5=0`.
Hence, `vecn_(1) bot vecn_(2)`.
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RS AGGARWAL-THE PLANE-Exercise 28B
  1. For each of the following planes, find the direction cosines of the no...

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  2. Find the vector and Cartesian equations of the plane passing throgh th...

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  3. Find the coordinates of the foot of the perpendicular drawn from the o...

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  4. Find the co-ordinates of the foot of perpendicular and the length of p...

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  5. Find the length of the foot of the perpendicular from the point (1,1,2...

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  6. From the point P(1,2,4) a perpendicular is drawn on the plane 2x+y-2z+...

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  7. Find the coordinates of the foot of the perpendicular and the perpendi...

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  8. Find the coordinates of the image of the point P(1, 3, 4) in the plane...

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  9. Find the point where the line (x-1)/2=(y-2)/-3=(z+3)/4 meets the plane...

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  10. find the coordinates of point where the line through (3,-4,-5) and (2,...

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  11. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

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  12. Find the distance of the point (0,-3,2) from the plane 3x+2y+2z+5=0, ...

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  13. Find the equation of the line passing through the point "P"(4,6,2) ...

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  14. Show that the distance of the point of intersection of the line (x-2)/...

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  15. Find the distance of the point (-1,-5,-10) from the point of the inter...

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  16. Prove tht the normals to the planes 4x+11y+2z+3=0 and 3x-2y+5z=8 are p...

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  17. Show that the line vecr=(2hati-2hatj+3hatk)+lambda(hati-hatj+4hatk) is...

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  18. Find the equation of a plane which is at a distance of 3\ sqrt(3) unit...

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  19. A vector vec n f magnitude 8 units is inclined to x-axis at 45^0 , y-...

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  20. Find the equation of a line passing through the point (2hati-3hatj-5h...

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