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If the vector equation of a line (x-2)/2...

If the vector equation of a line `(x-2)/2=(2y-5)/(-3) =z+1` is `vecr=2hati+5/2hatj-hatk+lambda(2hati-3/2 hatj+phatk)` then p is equal to

A

0

B

1

C

2

D

3

Text Solution

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The correct Answer is:
B
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The perpendicular distance of the point whose position vector is (1,3,5) from the line barr=hati+2 hatj+3 hatk+lambda(hati+2 hatj+2 hatk) is equal to

Find the angle between the line vecr=(2hati+2hatj+hatk)+lambda(2hati-3hatj+2hatk) and the plane vecr.(3hati-2hatj+5hatk)=4

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6 .

Find the vector equation of the following planes in cartesian form : " "vecr=hati-hatj+lamda(hati+hatj+hatk)+mu(hati-2hatj+3hatk) .

Find the equation of the plane which contains the line of intersection of the planes vecr.(hati+2hatj+3hatk)-4=0 and vecr.(2hati+hatj-hatk)+5=0 and which is perpendicular to the plane vecr.(5hati+3hatj-6hatk)+8=0

Find the parametric form of vector equation, and Cartesian equations of the plane containing the line vecr=(hati-hatj+3hatk)+t(2hati-hatj+4hatk) and perpendicular to plane vecr*(hati+2hatj+hatk)=8 .

Find the unit vector in the direction of the sum of vectors , veca=2hati+2hatj-5hatkandvecb=2hati+hatj+3hatk .

Find the shortest distance between the lines whose vector equations are vecr=(hati+2hatj+3hatk)+lambda(hati-3hatj+2hatk) and vecr=4hati+5hatj+6hatk+mu(2hati+3hatj+hatk)

Show that the line of intersection of the planes vecr*(hati+2hatj+3hatk)=0 and vecr*(3hati+2hatj+hatk)=0 is equally inclined to hati and hatk . Also find the angleit makes with hatj .

NEW JOYTHI PUBLICATION-THREE DIMENSIONAL GEOMETRY-Objective
  1. A unit vector parallel to the straight line (x-2)/3=(3+y)/(-1) = (z-2)...

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  2. The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d will be perpendicul...

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  3. If the vector equation of a line (x-2)/2=(2y-5)/(-3) =z+1 is vecr=2hat...

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  4. If the staight line (x-1)/k=(y-2)/2=(z-3)/3 and (x-2)/3=(y-3)/k =(z-1)...

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  5. The equation of the line joining the points (-3,4,11) and (1,-2,7) is

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  6. The vector equation of the line 6x-3=3y+4=2z-2 is

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  7. The angle between the staight lines (x+1)/2=(y-2)/5=(z+3)/4 and (x-1)/...

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  8. If the lines (x-1)/(-3)=(y-2)/(2k) =(z-3)/2 and (x-1)/(3k) =(y-5)/1=(z...

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  9. A line makes angles alpha,beta,gamma with the coordinates axes . If al...

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  10. The angle between the lines x=1,y=2 and y=-1 ,z=0 is

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  11. The distance between the lines vecr=veca1+tvecb and vecr=veca2+svecb i...

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  12. The vector equation of a plane which is at a distance of 6/sqrt29 from...

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  13. The equation of a plane with intercepts 2,3,and 4 on the x,y and z axe...

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  14. The direction cosines of the normal to the plane 6x-2y-2z=1 are

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  15. The distance of the point (2,1,-1) from the plane x-2y+4z=9 is

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  16. If the plane 2x-y+z=0 is parallel to the line (2x-1)/2=(2-y)/2 =(z+1)/...

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  17. The equation of the plane passing through (2,3,4) and parallel to the ...

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  18. The vector equation of the plane through the point (2,1,-1) and parall...

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  19. The equation of the plane passing through (1,2,3) and parallel to 3x-2...

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  20. The staight line passing through the point (1,0,-2) and perpendicular ...

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