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Find the angle between the lines vecr=...

Find the angle between the lines
`vecr=3hati-2hatj+6hatk+lamda(2hati+hatj+2hatk)` and `vecr=(2hatj-5hatk)+mu(6hati+3hatj+2hatk)`.

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To find the angle between the given lines, we can follow these steps: ### Step 1: Identify the direction vectors of the lines The first line is given by: \[ \vec{r} = (3\hat{i} - 2\hat{j} + 6\hat{k}) + \lambda(2\hat{i} + \hat{j} + 2\hat{k}) \] The direction vector \( \vec{b_1} \) for this line is: ...
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Find the shortest distance between the lines vecr=(hatii+2hatj+hatk)+lamda(2hati+hatj=2hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk) .

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Find the angle between the line vecr=(hati+2hatj-hatk)+lamda(hati-hatj+hatk) and the plane ver.(2hati-hatj+hatk)=4

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NCERT EXEMPLAR ENGLISH-THREE DIMENSIONAL GEOMETRY-LONG ANSWER TYPE QUESTIONS
  1. Find the angle between the lines vecr=3hati-2hatj+6hatk+lamda(2hati+...

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  2. Find the foot of the perpendicular from the point (2,3,-8) to the line...

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  3. Find the equation of the perpendicular drawn from (2,4,-1) to the line...

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

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  5. Find the equations of the line passing through the point (3,0,1) paral...

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  6. Find the shortest distance between the lines gives by vecr=(8+3lamda...

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  7. Find the equation of the plane which is perpendicular to the plane ...

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  8. The plane ax + by = 0 is rotated about its line of intersection with ...

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  9. Find the equation of the plane through the points (2, 1, 1) and (1, ...

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  10. Find the foot of perpendicular from the point (2,3,-8) to the line. ...

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  11. Find the distance of a point (2,4,-1) from the line (x+5)/1=(y+3)/4=...

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

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  13. Find the equations of the line passing through the point (3,0,1) paral...

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  14. Find the shortest distance between the lines gives by vecr=(8+3lamda...

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  15. Find the equation of the plane which is perpendicular to the plane ...

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  16. The plane ax + by = 0 is rotated about its line of intersection with ...

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  17. Find the equation of the plane through the points (2, 1, 1) and (1, ...

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