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Find the vector equation o the line pass...

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

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The correct Answer is:
`vec(r) = (hati + hatj + 3 hatk ) + lambda (-3 hati + 5 hatj + 4 hatk)`
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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 and cartesian equation of the line passing through the point P (1,2,3) and parallel to the planes : vec(r).(hati - hatj + 2 hatk) = 5. vec(r).(3hati + hatj + hatk) = 6.

Find the vector equation of a lie passing through the origin perpendicular to the plane vecr.(hati+2hatj+3hatk)=3 .

Find the vector equation of a line passing through the point A(1,-1,2) and perpendicular to the plane vecr.(2hati-hatj+3hatk)=5 .

Find the vector equation of a plane passing through the intersection of the planes vecr.(hati+hatj+hatk) = 6 and vecr. (2hati+3hatj+4hatk) - 5 = 0 and through the point (2,2,1) .

Find the vector equation of the plane passing through the intersection of the planes vecr.(2hati+2hatj-3hatk)=7, vecr.(2hati+5hatj+3hatk)=9 and the point (2,1,3) .

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

Find vector equations of the plane passing through A(-2,7,5) and parallel to vectors 4 hati -hatj +3hatk and hati +hatj -hatk .

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(2hati+3hatj-hatk)+4=0 and parallel to x-axis.

The angle between the planes vecr.(2hati-hatj+hatk)=6 and vecr.(hati+hatj+2hatk)=5 is

MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -REVISION EXERCISE
  1. If the direction cosines of a variable line in two adjacent points be ...

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  2. Prove that the straight lines whose direction cosines are given by the...

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  3. Prove that the line joining the mid-points of the two sides of a tr...

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  4. Find the vector equation of the line passing through (1, 2, 3) and ...

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  5. Prove that the lines x=ay +b,z =cy +d and x=a'y +b' z =c'y +a' ...

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  6. Prove that the line joining the points vec(6a) - vec(4b) + vec(4c) and...

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  7. Find the vector equation o the line passing through (1,2,3) and parall...

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  8. Find the vector equation of the line passing through the point (1,"...

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  9. find the coordinates of point where the line through (3,-4,-5) and (2,...

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  10. Show that equation of the plane passing through a point having positio...

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  11. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

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  12. Find the distance of the point with position vector - hati - 5 hatj - ...

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  13. Find the point R, Where the line joining P (1,3,4) and Q (-3,5,2) cuts...

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  14. Find the equation of the plane passing through the line of intersectio...

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  15. If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Z...

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  16. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

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  17. Find the equation of the plane , which contains the line of intersecti...

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  18. Prove that the shortest distance between the diagonals of a rectangula...

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  19. A variable plane is at a constant distance p from the origin and meets...

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