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Find the equation of a straight line passing through the point of intersection of the straight line `vecr=(2hati+4hatj-3hatk)+t(hati+2hatj+4hatk) and (x-1)/(2)=(y-3)/(3)=(z+1)/(2)` and perpendicular to both the straight lines.

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Find the parametric form of vector equation of a straight line passing through the point of intersection of the straight lines vecr=(hati+3hatj-hatk)+t(2hati+3hatj+2hatk) and (x-2)/(1)=(y-4)/(2)=(z+3)/(4) and perpendicular to both straight lines.

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.

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

Find the equation of the plane passing through the line of intersection of the plane vecr*(2hati+3hatj-4hatk)+1=0 and vecr*(hati-hatj+3hatk) =3 and through the point (1, 1, -1).

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

Find the equation of the plane through the intersection of the line 2x+3y=1 and vecr*(3hati-4hatj+3hatk)=8 and is parallel to the line (x-1)/(1)=(y-3)/(2)=(z+1)/(-1) .

Find the angle between the straight line vecr=(2hati+3hatj+hatk)+k+t(hati-hatj+hatk) and the plane 2x-y+z=5

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

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

PREMIERS PUBLISHERS-APPLICATIONS OF VECTOR ALGEBRA-PROBLEMS FOR PRACTICE (Answer the following questions)
  1. Find the equation of a straight line passing through the point of inte...

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  2. Prove that the sum of the squares of the squares of tha diagonals of a...

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  3. Show that (veca xx vecb) *(vecc xx vecd) +(vecb xx vecc) *(veca xx vec...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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