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The equation of line passing through the...

The equation of line passing through the point: (2,-1,4) and in the direction of `hati+hatj-2hatk` in cartesian form is :

A

1) `(x-2)/1=(y+1)/1=(z-4)/-2`

B

2) `(x-2)/1=(y+1)/1=(z+4)/-2`

C

3) `(x+2)/1=(y-1)/1=(z-4)/-2`

D

4) none of these

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Find the vector equation of a line passing through the point with position vector hati-2hatj-3hatk and parallel to the line joining the points with position vectors hati-hatj+4hatk and 2hati+hatj+2hatk . Also find the cartesian form of the equation.

Find the equation of the line passing through the point (2, -1, 3) and perpendicular to the lines : vecr=(hati-hatj+hatk)+lambda(2hati+hatj-3hatk) and vecr=(hati+hatj-hatk)+mu(hati+hatj+hatk)

Find the equation of the line passing through the point with position vector hati-hatj+2hatk and perpendicular to the plane vecr.(2hati-hatj+3hatk)=5 .

Find the equation of the line passing through the point (1,2,-3) and perpendicular to the lines : vecr=(2hati-hatj-hatk)+lambda(2hati-hatj-3hatk) and vecr=(3hati-hatj-2hatk)+mu(hati+hatj+hatk)

Find the vector equation of a line passing through the point with position vector (2hati-3hatj-5hatk) and perpendicular to the plane vecr*(6hati-3hatj-5hatk)+2=0 . Also, find the point of intersection of this line and the plane.

Find the equation of the line passing through the point (1,-2,3) and perpendicular to the lines : vecr=(hati-2hatj+hatk)+lambda(hati+hatj+hatk) and vecr=(hati-hatj+2hatk)+mu(3hati-2hatj-5hatk)

Find the equation of the plane passing through the point (1,1,1) and containing the line: vecr=(-3hati+hatj+5hatk)+lambda (3hati-hatj+5hatk) . Also, show that the plane contains the line: vecr=(-hati+2hatj+5hatk)+lambda(hati-2hatj-5hatk) .

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3hati + 2hatj - 2hatk

Find the vector equation of the line passing through the point (3,1,2) and perpendicular to the plane vecr*2hati-hatj+hatk)=4 . Also find the point of intersection of this line and the plane.

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. The direction cosines of the line whose direction ratios are 6,-2,3 :

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  2. The direction cosines of the line joining the points (-2,1,-8) and (4,...

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  3. The equation of line passing through the point: (2,-1,4) and in the di...

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

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

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  6. The direction ratios of a line normal to the plane x+2y-3z+4=0 are

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  7. Find the equation of the plane with interceots 2, 3 and 4 on the x, y ...

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

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  9. If the line (x-4)/(1)=(y-2)/(1)=(z-k)/(2) lies exactly on the plane 2x...

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  10. The point which lies in the plane given by the equations 2x+y-3z=10 is...

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  11. The angle between two planes : 3x-6y+2z=7 and 2x+2y-2z=5 is :

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  12. Direction cosines of the normal to the plane: 2x-3y+4z-6=0 are :

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  13. If a vector makes angles alpha, beta, gamma with x, y and z axes respe...

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  14. If a line makes angles of 90^@,60^@ and 30^@ with the positive x, y an...

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  15. The direction cosines of the line joining the points (-2, 4, -5) and (...

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  16. Distance between plane defined by 3x + 4y + 5 = 0 and the point (5, 0,...

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  17. Vector equation of the line (x+1)/(2)=(y-4)/(4)=(z+6)/(3)

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  18. The value of lambda for which the plane vecr*(2hati-2hatj+4hatk)=5 is ...

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  19. Direction casines of z-axis are

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  20. If a line has direction ratios <2,-1,-2>, then what are its direction ...

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