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Given the vector equation of a line as v...

Given the vector equation of a line as `vecr=(2hati-hatj+3hatk)+t(hati-hatj-hatk)` find the direction cosines of the line. Find also the equation of the line in non parametric form and in cartesian form.

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The correct Answer is:
cartesian form is `(x-2)/(1)=(y+1)/(-1)=(z-3)/(-1)`
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The vector equation in parametric form of a line is vecr=(3hati-2hatj+6hatk)+t(2hati-hatj+3hatk) . Find (i) the direction cosines of the straight line (ii) vector equation in non-parametric form of the line (iii) Cartesian equations of the line.

Show that the lines vecr=(-2hati-4hatj-6hatk)+t(hati+4hatj+7hatk) vecr=(hati+3hatj+5hatk)+s(3hati+5hatj+7hatk) are coplanar. Find the equation of such plane in non parametric form and in cartesian form.

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

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

The angle between the line vecr=(hati+2hatj-3hatk)+t(2hati+hatj-2hatk) and the plane vecr*(hati+hatj)+4=0 is :

Find the angle between the line vecr=(2hati-hatj+2hatk)+t(hati+2hatj-2hatk) and the plane vecr*(6hati+3hatj+2hatk)=8 .

Find the projection of the vector hati+3hatj+7hatk on the vector 2hati+6hatj+3hatk .

Find the angle between the straight line vecr=3hati-hatj+2hatk+t(2hati-hatj-2hatk) and the line joining the points (2, -1, 3) (-1, -2, 4).

Find the distance between the parallel planes vecr*(-hati-hatj+hatk)=3, vecr*(hati+hatj-hatk)=5 .

PREMIERS PUBLISHERS-APPLICATIONS OF VECTOR ALGEBRA-PROBLEMS FOR PRACTICE (Answer the following questions)
  1. Given the vector equation of a line as vecr=(2hati-hatj+3hatk)+t(hati-...

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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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