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Find the image of the point (1,3,4) in t...

Find the image of the point `(1,3,4)` in the plane `2x-y+z+3=0.`

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To find the image of the point \( (1, 3, 4) \) in the plane given by the equation \( 2x - y + z + 3 = 0 \), we can follow these steps: ### Step 1: Identify the coefficients of the plane equation The plane equation can be rewritten in the form \( ax + by + cz + d = 0 \): - Here, \( a = 2 \), \( b = -1 \), \( c = 1 \), and \( d = 3 \). ### Step 2: Write down the coordinates of the point The coordinates of the point are: ...
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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Write the equation of the plane whose intercepts on the coordinate axe...

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  2. Show that the four point (0,-1,-1),(4,5,1),(3,9,4)a n d(-4,4,4) are co...

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  3. Find the image of the point (1,3,4) in the plane 2x-y+z+3=0.

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  4. Find the image of the point with position vector 3 hat i+ hat j+2 hat ...

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  5. Find the length and the foot of perpendicular from the point (1,3//...

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  6. Find the distance between the point with position vector hat i-5 hat ...

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

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  8. Show that the plane whose vector equation is vec rdot( hat i+2 hat j-...

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  9. Prove that the lines (x+1)/3=(y+3)/5=(z+5)/7a n d(x-2)/1=(y-4)/4=(z-6)...

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  10. Show that the lines vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat ...

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  11. Find the distance of the point P(-1,-5,-10) from the point of intersec...

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  12. Find the distance of the point (1,-2,3) from the plane x-y+z=5 measure...

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  13. Show that the plane whose vector equation is vec r*( hat i+2 hat j= h...

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  14. Find the equation of the plane passing through the point (0,7,-7) and...

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  15. Find the equation of the plane passing through the points (1,-1,2)a n ...

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  16. Find the equation of the plane passing through the point whose coor...

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  17. Find the equation of the plane passing through the point (1,1,-1)a n d...

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  18. Find the equation of the plane passing through the point (-1,-1,2)a n ...

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  19. Find the angle between the planes x+y+2z=9a d n2x-y+z=15.

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  20. If the planes Find the angle between the planes vec rdot(2 hat i- hat...

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