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

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The correct Answer is:
`vec(r) = ( 1 + lambda) hati + 2 (1 + lambda ) hatj + (3 - 5 lambda) hatk.`
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Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane -> r(dot( hat i+2 hat j-5 hat k))=9.

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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.

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.

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

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

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MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -EXERCISE 11 (F) (LONG ANSWER TYPE QUESTIONS (I) )
  1. (i) show that the line : vec(r) = 2 hati - 3 hatj + 5 hatk + lambda ...

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  2. Find the value of 'm' for which the line vec(r) = ( hati + 2 hatk ) + ...

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  3. Find the vector equationof the line passing through the point (3,1,2) ...

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  4. Find the coordinates of the point where the line ("x"+1"\ ")/2=("y"...

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  5. (i) Find the angle between the line : ( 2 hati + 3 hatj + 4 hatk ) ...

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  6. (i) Find the angle between the line : (x + 1)/(2) = (y)/(3) = (z - 3...

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  7. Find the distance of the points (-1, -5, -10) form the point of inters...

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

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

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  10. Find the vector and cartesian equation of the line passing through th...

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

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  12. Find the Cartesian equation of the plane passing through the points...

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  13. Find the equation of the plane through the points (1,0,-1),(3,2,2) and...

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  14. Find the equation of the plane containing the line. : (x + 2)/(2) = ...

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  15. Find the equation of the plane which contains two parallel to lines (x...

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  16. Find the vector and cartesian equations of the plane containing the li...

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  17. Find the equation of the plane through the point (1,1,1) and perpendic...

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  18. The line draw from points (4,-1,2) to the points (-3,2,3)meets and a p...

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  19. (a) Find the length and the foot of the perpendicular from : P (1,1,...

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  20. Find the co-ordinates of the foot of the perpendicular from the point ...

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