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Show that the line , vecr=2hati-3hatj+5h...

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

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

True or false The line vecr=2hati-3hatj+hatk+t(hati-hatj+2hatk) lies in the plane vecr.(3hati+hatj-hatk)-2=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 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+3hatk) and the plane vecr*(2hati+hatj-hatk)=4 . Also find whether the line is parallel to the plane or not.

Find the angle between the line vecr=(hati-hatj+3hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(hati+hatj+2hatk) =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 (-1 , -5 , -10) from the point of intersection of the line vecr=2hati-hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr.(hati-hatj+hatk) =5.

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

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 .

ACCURATE PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTIONS CARRYING 1 MARK (TYPE-III: (TRUE OR FALSE QUESTIONS))
  1. The points (1, 2, 3), (-2, 3, 4) and (7,0,1) are collinear.

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  2. The vector equation of the line passing through the points (3,5, 4) an...

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

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

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  5. Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) li...

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

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

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  8. If the foot of perpendicular drawn from the origin to a plane is (5,-3...

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  9. A line can have 45^(@),60^(@),120^(@) as direction angles.

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  10. A line can have 45^(@),60^(@),120^(@) as direction angles.

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  11. If a line makes an angle of (pi)/(4) each of y and z axis, then the an...

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  12. Write the direction cosine of a line parallel to the line : (3-x)/3=(y...

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  13. Show that the lines (x-5)/7 = (y+2)/-5 = z/1 and x/1 = y/2 = z/3 are p...

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  14. The shortest distance between two parallel line vec(r)(2)=vec(a)(1)+la...

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  15. Find the intercepts cut off by the plane 2x+y-z = 5

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  16. Find the value of k for whicj the planes: 3x-6y-2z=7 and 2x+y-kz=5 are...

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  17. The planes 2x - y + 4z = 5 and 5x - 2.5y + 10z = 6 are :

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