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Write the vector equation fo the line pa...

Write the vector equation fo the line passing through the point (1,-2,-3) and normal to the plane `vec(r). (2 hati + hatj + 2 hatk)` = 5 .

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The correct Answer is:
`vec(r) = hati - 2 hatj - 3 hatk + lambda ( 2 hati + hatj + 2 hatk)`
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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.

(i) Find the vector equation of the line passing through (1,2,3) and parallel to the planes : vec(r) . (hati - hatj + 2 hatk ) = 5 and vec(r) . (3 hati + hatj + hatk) = 6 . (ii) Find the vector equation of the straight line passing through (1,2,3) and perpendicular to the plane : vec(r) . (hati + 2 hatj - 5 hatk ) + 9 = 0 .

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 .

(i) Find the equations of the plane passing through (a,b,c) and parallel to the plane vec(r) . (hati + hatj + hatk) = 2 . (ii) Find the vector equation of the plane through the point hati + hatj + hatk and parallel to the plane vec(r). (2 hati - hatj + 2 hatk) = 5 .

The equation of a line passing through the point (4,-2,5) and parallel to the vector 3hati -hatj + 2hatk is

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

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

The equation of the plane passing through the point (2, -1, 3) and perpendicular to the vector 3hati + 2hatj - hatk is

Find the vector and cartesian equations of the plane that passes through the point (0, 1, -2) and normal to the vector hati + hatj + hatk .

Find the vector and cartesian equation of plane which passes through the point (1,3,-2) and normal to the vector (2hati+hatj-2hatk) .

MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -OBJECTIVE TYPE QUESTIONS (D. VERY SHORT ANSWER TYPE QUESTIONS )
  1. If a line makes angle 90^(@) and 60^(@) respectively with positively d...

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  2. Find the direction-cosines of the line (x - 1)/(2) = - y = (z + 1)/...

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  3. Write the vector equation of the line : (x - 5)/(3) = (y + 4)/(7) = ...

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  4. The cartesian equations of line is : (x - 1)/(2) = (y - 2)/(3) = (z ...

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  5. Find the vector equation of the line which passes through the point (3...

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  6. Find the length of the perpendicular drawn from the point P (3, -4, 5)...

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  7. The equation of a line given by (4-x)/3=(y+3)/3=(z+2)/6dot Write the d...

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  8. Find the cartesian equation of the line which passes through the poin...

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  9. Find the acute angle between the plane : vec(r). (hati - 2hatj - 2 h...

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  10. Write the equation of the plane passing through (a , b , c) and parall...

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  11. Write the intercept cut off by the plane 2x+y-z=5 on x-axis.

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  12. Find the vector equation of a plane which is at a distance of 5 units...

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  13. Find the vector equations of the plane whose cartesian form of equatio...

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  14. Find the cartesian equation of the plane vec(r). (2 hati + 3 hatj - 4 ...

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  15. What are the direction-cosines of the normal to the plane 3x + 2y - 3z...

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  16. Find the direction-cosines of the perpendicular from the origin to the...

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  17. Find the the distance of a point (2,5, -3) from the plane vec(r).(6 ha...

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  18. Find the value of 'k' for which the plane : 3x - 6y - 2z = 7 and 2x...

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  19. Write the vector equation fo the line passing through the point (1,-2,...

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  20. Write the equation of a plane which is at a distance of 5sqrt(3) units...

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