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The vector equation of the line passing ...

The vector equation of the line passing through the points (3,5, 4) and (5, 8, 11) is
`vecr=3hati+5hatj+4hatk+lamda(2hati+3hatj+7hatk)`

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Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-hatk) .

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 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 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 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 vector equation of the plane passing through the intersection of the planes vecr.(hati+hatj+hatk) =6 and vecr.(2hati+3hatj+4hatk)=-5 and point (1,1,1)

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 equation in vector anf cartesian form of the line passing through the point : (2,-1,3) and perpendicular to the lines vecr= (hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr= (2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

Find the vectoer and cartesian equations of the line through the point (1,2,-4) and perpendicualr of the lines: vecr=(8hati-19hatj+10hatk)+lambda(3hati-16hatj+7hatk) and vecr=(15hati+29hatj+5hatk)+mu(3hati+8hatj-5hatk)

Find the vector equation of the plane passing through the intersection of the planes vecr cdot (hati+hatj+hatk) = 6 and vecr cdot(2hati + 3hatj+4hatk) = -5 , and the point (1, 1, 1).

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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