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Find the equation of the straight line p...

Find the equation of the straight line passing through the point (2,-1,3) and perpendicular to the lines
`vec(r)=(hat(i)+hat(j)-hat(k))+lamda(2hat(i)+hat(j)-3hat(k))` and `vec(r)=(hat(i)-hat(j)-hat(k))+mu(hat(i)+hat(j)+hat(k))`.

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The correct Answer is:
`(x-2)/(4)=(y+1)/(-5)=(z-3)/(1)`
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Find the shortest distance between the following lines vec(r)=hat(i)+hat(j)-2hat(k)+lamda(hat(i)+hat(j)+hat(k)) and vec(r)=hat(i)+hat(j)+hat(k)+mu(hat(i)+hat(j)+hat(k))

BETTER CHOICE PUBLICATION-THREE DIMENSIONAL GEOMETRY -PREVIOUS YEARS BOARD.S QUESTION FOR PRACTICE
  1. Find the equation of the plane passing through the points (1,1,0),(1...

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  2. Find the direction cosine of a line parallel to the line (2x-5)/(4)=(y...

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  3. Find the equation of the straight line passing through the point (2,-1...

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  4. Find the equation of a plane through the points (1,0,1),(1,2,-2),(2,...

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  5. Find the equation of a plane passing through the points (1,1,2) and (1...

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  6. Find the equation of the plane through the point (-1, -1, 2) and (3, 4...

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  7. Find the equation of the plane passing through the point(-1, 3, 2) and...

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  8. A variable plane which is at a constant 6 p from the origin meets the ...

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  9. Show that the lines (x-1)/(2)=(y-3)/(4)=-z and (x-4)/(2)=(y-1)/(-2)=(z...

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  10. Show that the lines (x+3)/-3=(y-1)/1=(z-5)/5 and (x+1)/-1=(y-2)/2=(z-5...

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  11. Prove that the lines : (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-2)/(3)=(y-...

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

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  13. Find the vector equation of the plane through the intersection of the ...

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

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  15. Find the equation of the straight line through the point (1,-3,2) and ...

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  16. Find the equation of the straight line passing through the point (2,3,...

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  17. Find the shortest distance between the line vec(r)=hat(i)-7hat(j)-2hat...

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  18. Find the equation of the plane through the point (1,1,1), parallel to ...

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  19. Find the distance between the point with position vector -hat(i)-5hat(...

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  20. Show that the two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-4)/5=(y-1)/2=z ...

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