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A line with cosines proportional to 2,7-...

A line with cosines proportional to `2,7-5` drawn to intersect the lines `(x-5)/3=(y-7)/-1=(z+2)/1 ; (x+3)/-3=(y-3)/2=(z-6)/4` .Find the co- ordinates of the points of intersection and the length intercepted on it.

A

`sqrt(78)`

B

`sqrt(77)`

C

`sqrt(54)`

D

`sqrt(74)`

Text Solution

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The correct Answer is:
A
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MCGROW HILL PUBLICATION-THE DIMENSIONAL GEOMETRY -EXERCISE (LEVEL 1 (SINGLE CORRECT ANSWER TYPE QUESTIONS))
  1. Prove that the lines (x+1)/3=(y+3)/5=(z+5)/7a n d(x-2)/1=(y-4)/4=(z-6)...

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  2. Equation of a plane bisecting an angle between the plane r.(i+2j+2k)=1...

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  3. If the line (x-1)/(2)=(y-3)/(a)=(z+1)/(3) lies in the plane bx+2y+3z-4...

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  4. Equation of the plane passing through the points i+j-2k,2i-j+kandi+2j+...

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  5. The line of shortest distance between the lines (x-1)/(2)=(y+8)/(-7)...

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  6. If r.n=q is the equation of a plane normal to the vector n, the length...

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  7. If the foot of the perpendicular from the origin to plane is P(a ,b...

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  8. The plane passing through the point (-2,-2, 2) and containing the line...

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  9. Equation of a line passing through the point whose position vector is ...

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  10. The lines r=i-j+lambda(2i+k) and r=2i-j+mu(i+j-k)

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  11. The points (-2,5), (3, -4) and (7, 10) are the vertices of the triangl...

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  12. The foot of the perpendicular from (a, b, c) on the line x=y=z is the ...

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  13. Equation of a plane which passes through the line x+py+q=0=rz+s and ma...

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  14. Parametric form of the equation of the line 3x-6y-2z-15=2x+y-2z-5=0 is

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  15. A line with cosines proportional to 2,7-5 drawn to intersect the lines...

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  16. The YZ-plane divides the line joining the points (3,5,-7)and(-2,1,8) i...

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  17. Find the angle between the lines (x-2)/3=(y+1)/(-2)=z=2a n d(x-1)/1=(2...

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  18. If the plane (x)/(a)+(y)/(b)+(y)/(c )=3 meets the coordinate axes in A...

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  19. The variable plane (2lambda+1)x+(3-lambda)y+z=4 always passes through ...

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  20. Algebraic sum of the intercepts by the plane 3x-4y+7z=84 on the axes i...

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