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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 .

i.Find the cartesian equation of the plane passing through the point (1,2,-3) and perpendicular to the vector 2hati-hatj+2hatk . ii. Find the angle between the above plane and the line (x-1)/2=(y-3)/3 =z/6 .

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 .

FULL MARKS-APPLICATIONS OF VECTOR ALGEBRA-Additional Questions Solved
  1. Find the vector and cartesian equations of the plane passing through t...

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  2. Find the vector and cartesian equations of the plane passing through t...

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

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  4. Find the vector and cartesian equations of the plane containing the li...

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  5. Derive the equation of the plane in the intercept form.

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  6. Find the Cartesian form of the equation of the plane vec(r)=(s-2t)hat(...

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  7. Show that the straigh lines vecr=(veci+vecj-veck)+lambda(3veci-vecj)...

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  8. If the straight lines (x-1)/(2)=(y+1)/(lamda)=(z)/(2)and(x+1)/(5)=(y+1...

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  9. If the lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/...

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  10. Show that the lines (x+3)/(-3)=(y-1)/(1)=(z-5)/(5) and (x+1)/(-1)...

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  11. Find the point of intersection of the line passing through the two poi...

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

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  13. Find the point of intersection of the line vecr=(vecj-veck)+s(2veci-...

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  14. Find the meeting point of the line vecr=(2veci+vecj-3veck)+t(2veci-v...

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  15. Show that the following planes are at right angles: vecr.(2veci+vec...

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  16. The planes vecr.(2vec+lambdavecj-3veck)=10 and vecr.(lambdavec+3ve...

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  17. Find the angle between the line (x-2)/(3)=(y-1)/(-1)=(z-3)/(2)" and th...

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  18. Find the angle between the line vecr=veci+vecj+3veck+lambda(2veci+ve...

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  19. If veca=2veci+vecj-veck , vecb=veci+2vecj+veck and vecc=veci-v...

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  20. If veca=hati-hatk,vecb=xhati+hatj+(1-x)hatk,vecc=yhati+xhatj+(1+x-y)h...

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