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Find the vector and certesian equation of the plane through the points (1, 2, 3) and (2, 3, 1) and perpendicular to the plane `vecr*(3hati-2hatj+4hatk)=5`.

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Find the vector cartesian equation of the plane passing through the points (1, -2, 3) and (-1, 2, -1) and is parallel to the line vecr=(2hati-hatj+hatk)+t(2hati+3hatj+4hatk)

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

Find the vector equation and cartesian equation of the line through the point (1, 2, -2) and in parallel to (3hati-4hatj+5hatk) .

Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3hati+2hatj-8hatk .

Find the non parametric form of vector equation and the cartesian equation of the plane passing through the point (-1, 2, -3) and parallel to the lines vecr=(2hati-hatj+3hatk)+t(hati+hatj-2hatk) and vecr=(hati-hatj+3hatk)+s(3hati-hatj-2hatk)

Find the vector and cartesian equation of the plane through the point whose position vector is 2hati-3hatj+hatk and normal to the vector 3hati-2hatj-hatk .

Find the vector and cartesian equations of the planes a. that passes through the point (1,0,-2) and normal to the planes is hati+hatj-hatk b. that passes through the point (1,4,6) and the normal vector to the plane is hati-2hatj+hatk .

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The vector equation of the plane through the point (2,1,-1) and parallel to the plane vecr.(hati+3hatj-hatk)=0 is

Find the Cartesian equation of the plane through the point with position vector 2hati-hatj+hatk and perpendicular to the vector 4hati+2hatj-3hatk .

PREMIERS PUBLISHERS-APPLICATIONS OF VECTOR ALGEBRA-PROBLEMS FOR PRACTICE (Answer the following questions)
  1. Show that (veca xx vecb) *(vecc xx vecd) +(vecb xx vecc) *(veca xx vec...

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  2. Find the vector and cartesian equation of the line through the point (...

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  3. Find the vector and cartesian equation of the line joining the points ...

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  4. Find the angle between the lines (x-1)/(2)=(y+1)/(3)=(z-4)/(6) and vec...

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  5. Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-...

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  6. Show that the lines vecr=(hati-hatj)+t(2hati+hatk) and vecr=(2hati-hat...

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  7. Find the vector and cartesian equation of a plane which is at a distan...

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  8. Find the vector and cartesian equation of the plane passing through (2...

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  9. Find the vector and cartesian equation of the plane passing through (2...

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  10. Find the Vector and Cartesian equation of the plane containing the lin...

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  11. Find the vector cartesian equation of the plane passing through the po...

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  12. Find the vector and certesian equation of the plane through the points...

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  13. Find the equation of the plane passing through the points (3, 4, 2), (...

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  14. Find the equation of the plane passingthrough the intersection of the...

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  15. Find the distance between the parallel planes vecr*(-hati-hatj+hatk)=3...

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  16. Find the coordinates of the point where the line vecr=(hati+2hatj-5ha...

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  17. The value of [hati+hatj,hatj+hatk,hatk+hati] is equal to :

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  18. If abs(veca+vecb)=abs(veca-vecb) prove that veca and vecb are perpendi...

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  19. Find the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3...

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  20. Show that the lines vecr=(4veci+5vecj+6veck)+t(2veci+3vecj+4veck) and ...

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