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Find the vector equation of the line pas...

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane `vecr cdot(hati+2hatj-5hatk) + 9 = 0`

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The correct Answer is:
`vec(r)=(hat(i)+2hat(j)+3hat(k))+lamda(hat(i)-2hat(j)-5hat(k))`
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Find the vector equation of the line passing through the point (1,2,1) and perpendicular to the plane vecr.(2hati-hatj+hatk)=10 . Find the point of intersection of this line and the plane.

Find the vector equation of the line passing through the point (3,1,2) and perpendicular to the plane vecr*2hati-hatj+hatk)=4 . Also find the point of intersection of this line and the plane.

Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes vecr = (hati-hatj+2 hatk)= 5" and "vecr *(3hati- hatj+hatk)= 6 . Also find the point of intersection of the line thus obtained with the plane vecr * (2hati-hatj+hatk)= 4 .

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 of the plane passing through (a, b, c) and parallel to the plane vecr cdot(hati + hatj + hatk) = 2

Find the vector equation of the line through the origin, which is perpendicular to the plane vecr*(hati-2hatj+hatk)=3 .

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

BETTER CHOICE PUBLICATION-THREE DIMENSIONAL GEOMETRY -PREVIOUS YEARS BOARD.S QUESTION FOR PRACTICE
  1. Show that the lines (x+3)/-3=(y-1)/1=(z-5)/5 and (x+1)/-1=(y-2)/2=(z-5...

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  2. Find the foot of perpendicular drawn from origin to the plane 2x+3y+4z...

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

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  4. Find the equation of the plane passing through (a, b, c) and parallel ...

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  5. Find the shortest distance between the lines whose vector equations ar...

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  6. Find the shortest distance between the lines whose vector equations ar...

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  7. Find the shortest distance between the lines whose vector equations ar...

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  8. Find the equation of the plane through the points (0,-1,0),(2,1,-1) an...

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  9. Find the equation of the plane passing through the points (0,-1,0),(1,...

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  10. Find the equation of the plane passing through the points (2,2,1), (9,...

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  11. Find the angle between the pair of lines (x+3)/3 = (y-1)/5 = (z+3)/4an...

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  12. Find the shortest distance between the lines vec(r)=hat(i)+hat(j)+la...

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  13. Find the coordinate of the point where the line through the points A(3...

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  14. Find the coordinate of the point where the line through the points A(3...

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  15. Find the coordinate of the point where the line through the points A(3...

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  16. Find the vector equation of the plane passing through the intersection...

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  17. Show that the points whose position vectors are -2hat(i)+3hat(j)+5hat(...

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  18. Find the image of the point (2,0,1) in the line (x-3)/(1)=(y+2)/(-2)...

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  19. Find the angle between the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (...

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  20. Find the equation of the plane through the points (2, 2, 1) and (9, 3...

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