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True or false The line vecr=2hati-3hatj+...

True or false
The line `vecr=2hati-3hatj+hatk+t(hati-hatj+2hatk)` lies in the plane `vecr.(3hati+hatj-hatk)-2=0`.

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Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) lies in the plane vecr*(3hati+hatj-hatk)+2=0 .

Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr*(hati+2hatj-hatk)=3 .

Find the distance of the point (2,12,5) from the point of intersection of the line: vecr=2hati-4hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr*(hati-2hatj+hatk)=0 .

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

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

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

Find the distance of the point with position vector -hati-5hatj-10hatk from the point of intersection of the line vecr=(2hati-hatj+2hatk)+lambda(3hati+4hatj+12hatk) and the plane vecr*(hati-hatj+hatk)=5 .

Find the distance of the point (2, 3, -1) from the point of intersection of the line vecr=3hati+hatj-2hatk+lambda(3hati+6hatj+2hatk) and the plane vecr.(2hati-hatj+hatk) =3.

Find the angles between the line vecr=-hati+hatj+2hatk+lambda(3hati+2hatj+4hatk) and the plane vecr.(2hati+hatj-3hatk)+4=0

Find the point of intersection of the line : vecr=(hati+2hatj+3hatk)+lambda(2hati+hatj+2hatk) and the plane vecr*(2hati-6hatj+3hatk)+5=0 .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. The unit vector normal to the plane x+2y+3z-6=0 is (1)/(sqrt14)hati+(2...

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  2. True or false The line x=y=z lies in the plane x-2y+z-1=0.

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  3. True or false The line vecr=2hati-3hatj+hatk+t(hati-hatj+2hatk) lies i...

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  4. True or false The projection of the point (alpha,beta,gamma) on the XO...

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  5. The intercepts made by the plane 2 x – 3 y + 5z+4 = 0 on the co-ordina...

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  6. True or false The projection of the point (alpha,beta,gamma) on the z-...

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  7. True or false The vector equation of the line (x-5)/3=(y+4)/7=(z-6)/2 ...

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  8. The acute angle between the planes vecr.(2hati-3hatj+hatk)=1 and vecr....

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  9. If ltl,m,n,gtare D. cosines of a line then l^(2)+m^(2)+n^(2)=

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  10. The angle between the lines vecr=(5hati-hatj-4hatk)+lambda(2hati-hatj+...

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  11. True or false The distance of the point (-2,4,-5) from the line (x+3)/...

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  12. Find equation of a plane passing through the points (2,1,0),(3,-2,-2) ...

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  13. The equation of a line, which is parallel to 2hati+hatj+3hatk and whic...

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  14. True or false If the foot of perpendicular drawn from the origin to a ...

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  15. Direction cosines of x-axis are

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  16. Direction cosines of any normal to xy-plane are

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  17. Distance of the point (alpha, beta,gamma) from y-axis is

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  18. The distance of a point P(a,b,c) from x axis is:

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  19. If the direction cosine of a line are < k,k,k >, then,

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  20. If a line makes angles alpha,beta,gamma respectively with positive dir...

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