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Distance of the point (2,5,-3) from the ...

Distance of the point (2,5,-3) from the plane `vec r.(6hat i-3 hat j+2 hat k)=4` is

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Find the distance of a point (2,5,-3) from the plane vec(R)*(6hat(i)-3hat(j)+2hat(k))=4

Find the distance of the points (2,3,4) from the plane vec(R)*(3hat(i)-6hat(j)+2hat(k))=-11 .

Find the distance between the following parallel planes vec r . (2 hat i - 3 hat j + 6 hat k) = 5 and vec r . (6 hat i - 9 hat j + 18 hat k) + 20 = 0 .

Find the shortest distance between the lines given by the equations vec r= (hat i - hat j + 2 hat k + lambda (2 hat i + hat j + 4 hat k) , vec r= (2 hat i - 4 hat j + hat k) + mu (3 hat i + hat j - 5 hat k) .

Find the distance of the point (-1,-5,-10) from the point of intersection of the line vec(r)=2hat(i)-hat(j)+2hat(k)+lamda(3hat(i)+4hat(j)+2hat(k)) and the plane vec(r)*(hat(i)-hat(j)+hat(k))=5

Find the shortest distance between the lines given by the equations vec r= (hat i - 2 hat j + 3 hat k) + lambda ( hat i +3 hat j + 4 hat k) , vec r= (2 hat i - hat j +5 hat k) + mu (3 hat i + 4 hat j - hat k) .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Write the vector equations of the plane throught the point (a,b,c) and...

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  2. If the cartesian equations of a line are : (3-x)/5=(y+4)/7=(2z-6)/4, w...

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  3. Distance of the point (2,5,-3) from the plane vec r.(6hat i-3 hat j+2 ...

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  4. Write down the direction cosines of the line whose equations are 5x-3=...

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  5. Write the sum of intercepts cut off by the plane vecr*(2hati+hatj-hatk...

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  6. If a line angles 90^@, 135^@, 45^@ with the positive x,y and z axis re...

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  7. Find the direction cosines of a line which makes equal angles with the...

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  8. If a line has the direction ratios –18, 12, – 4, then what are its dir...

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  9. Show that the points (2, 3, 4), (– 1, – 2, 1), (5, 8, 7) are collinear...

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  10. Find the direction cosines of the sides of the triangle whose vertices...

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  11. show that the three lines with direction cosines <12/13,-3/13,-4/13>, ...

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  12. Show that the line through the points (1, – 1, 2), (3, 4, – 2) is perp...

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  13. Show that the line through the points (4,7,8) and (2,3,4) is parallel ...

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  14. Find the equation of the line which passes through the point (1, 2, 3)...

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  15. Find the equation of the line in vector and in cartesian form that pas...

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  16. Find the cartesian equation of the line which passes through the point...

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  17. The cartesian equation of a line is (x-5)/3 = (y+4)/7 = (z-6)/2. Write...

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  18. Find the vector and the cartesian equations of the lines that passes t...

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  19. Find the vector and the cartesian equations of the line that passes th...

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  20. Find the angle between the following pair of lines: vecr = 2hati-5hatj...

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