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Find the direction cosines and length of...

Find the direction cosines and length of the perpendicular from hte origin to the plane `vecr*(12hati-4hatj-3hatk)=7`.

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The correct Answer is:
`((12)/(13), -(4)/(13), -(3)/(13)); (7)/(3)`
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Find the direction cosines of the normal to the plane and length of the perpendicular from the origin to the plane vecr.(3hati-4hatj+12hatk)=5 .

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Find the direction cosines of the unit vector perpendicular to the plane. vecr(6hati-3hatj-2hatk)+1=0

Find the perpendicular distance of the point (2, -3, 3) from the plane vecr*(hati-2hatj-2hatk)=8 .

Find the direction cosines of the vector hati+2hatj+3hatk .

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).

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PREMIERS PUBLISHERS-APPLICATIONS OF VECTOR ALGEBRA-PROBLEMS FOR PRACTICE (Answer the following questions)
  1. Find the direction cosines and length of the perpendicular from hte or...

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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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