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Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane ` vec r.( hat i+2 hat j-5 hat k)+9=0`.

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Given ,A Line passes through the point (1, 2, 3). and is perpendicular to the given plane.
Therefore, it is parallel to the line (- i+2j​−5k)
Therefore, equation of the required line is : `r = (i +2j ​+3k ) + λ(i ...
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Find the vector equation of the line passing through (1, 2, 3 ) and parallel to the planes vec rdot( (hat i- hat j+2 hat k)=5\ a n d\ vec rdot((3 hat i+ hat j+ hat k)=6.

Find the vector equation of the line through the origin which is perpendicular to the plane vec rdot(( hat i+2 hat j+3 hat k)=3.

Find the vector and Cartesian equations of the line passing through (1, 2, 3) and parallel to the planes vec rdot(( hat i- hat j+2 hat k)=5\ a n d\ vec rdot((3 hat i+ hat j+ hat k)=6.

Write the vector equation of the line passing through the point (1, -2, -3) and normal to the plane vec rdot((2 hat i+ hat j+2 hat k)=5.

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec r*(hat i-hat j+2hat k)=5 and vec r*(3hat i+hat j+hat k)=6

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Write the vector equation of the plane passing through the point (a,b,c) and parallel to the plane vec r.(hat i+hat j+hat k)=2

NCERT-THREE DIMENSIONAL GEOMETRY-MISCELLANEOUS EXERCISE
  1. If the points (1,1,p) a n d (3, 0, 1)be equidistant from the plane v...

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  2. Find the equation of the plane which contains the line of intersectio...

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  3. If O be the origin and the coordinates of P be(1, 2, -3), then find ...

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  4. Find the coordinates of the point where the line through (5, 1, 6) an...

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  5. Find the coordinates of the point where the line through (5, 1, 6) an...

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  6. Find the equation of the plane passing through the point ( 1, 3, 2)an...

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  7. Find the coordinates of the point where the line through (3, 4, 5)a...

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  8. The planes: 2x y + 4z = 5 a n d 5x 2. 5 y + 10 z = 6are(A) Perpendic...

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  9. Find the equation of the plane passing through (a, b, c) and parallel...

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  10. Find the shortest distance between lines vecr=6 hat i+2 hat j+ hat k...

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  11. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2and (x-1)/(3k)=(y-1)/1=(z-6...

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  12. Find the vector equation of the line passing through (1, 2, 3) and pe...

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  13. Find the equation of a line parallel to x-axis and passing through th...

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  14. If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7),...

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  15. If l1,m1,n1and l2,m2,n2are the direction cosines of two mutually per...

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  16. Find the angle between the lines whose direction ratios are a, b, c a...

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  17. Show that the line joining the origin to the point (2, 1, 1)is perpen...

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  18. Find the vector equation of the line passing through the point (1,2,-...

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  19. Prove that if a plane has the intercepts a, b, c and is at a distance...

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  20. Distance between the two planes: 2x + 3y + 4z = 4and 4x + 6y + 8z = 12...

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