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Write the sum of intercepts cut off by t...

Write the sum of intercepts cut off by the plane `vecr*(2hati+hatj-hatk)-5=0` on the three axes.

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Find the equations of the plane which contains the line of intersections of the planes vecr.(hati-2hatj+3hatk)-4=0 and vecr.(-2hati+hatj+hatk)+5=0 and whose intercept on x-axis is equal to the on y-axis.

Find the equation of the plane which contain the line of intersection of the plane vecr.(hati+2hatj+3hatk)-4=0 and vecr.(2hati+hatj-hatk)+5=0 and which is perpendicular to the plane 5x+3y-6z+8=0 .

Find the equation of the plane which contains the line of intersection of the planes vecr cdot(hati+2hatj+3hatk) - 4 = 0 and vecr cdot (2hati + hatj - hatk) +5 = 0 and which is perpendicular to the plane vecr cdot (5hati+3hatj-6hatk) +8 =0

Find the cartesian equation of the following planes. vecr.(hati+hatj-hatk)=2

Find a unit vector normal to the plane : vecr*(2hati-3hatj+6hatk)+14=0 .

Find the equation of the plane passing through the line of intersection of the planes vecr cdot (hati+hatj+hatk) = 1 and vecr cdot(2hati+3hatj-hatk)+4 = 0 and parallel to x-axis.

Find the equation of the plane passing through the line of intersection of the planes : vecr*(hati+3hatj)-6=0 and vecr*(3hati-hatj-4hatk)=0 , whose perpendicular distance form origin is unity.

Find the image of the point hati+3hatj+4hatk in the plane vecr.(2hati-hatj+hatk)+3=0 .

Find the vector equation of the plane passing through the intersection of the planes : vecr*(2hati-hatj+2hatk)=2 and vecr*(3hati+hatj-2hatk)=-2 and perpendicular to the veca=5hati-2hatj+3hatk .

Find the cartesian equation of the following planes: vecr.(hati+hatj+hatk)=2

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Distance of the point (2,5,-3) from the plane vec r.(6hat i-3 hat j+2 ...

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  2. Write down the direction cosines of the line whose equations are 5x-3=...

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  3. Write the sum of intercepts cut off by the plane vecr*(2hati+hatj-hatk...

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  4. If a line angles 90^@, 135^@, 45^@ with the positive x,y and z axis re...

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  5. Find the direction cosines of a line which makes equal angles with the...

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  6. If a line has the direction ratios –18, 12, – 4, then what are its dir...

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  7. Show that the points (2, 3, 4), (– 1, – 2, 1), (5, 8, 7) are collinear...

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  8. Find the direction cosines of the sides of the triangle whose vertices...

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  9. show that the three lines with direction cosines <12/13,-3/13,-4/13>, ...

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  10. Show that the line through the points (1, – 1, 2), (3, 4, – 2) is perp...

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  11. Show that the line through the points (4,7,8) and (2,3,4) is parallel ...

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  12. Find the equation of the line which passes through the point (1, 2, 3)...

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  13. Find the equation of the line in vector and in cartesian form that pas...

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  14. Find the cartesian equation of the line which passes through the point...

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  15. The cartesian equation of a line is (x-5)/3 = (y+4)/7 = (z-6)/2. Write...

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  16. Find the vector and the cartesian equations of the lines that passes t...

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  17. Find the vector and the cartesian equations of the line that passes th...

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  18. Find the angle between the following pair of lines: vecr = 2hati-5hatj...

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  19. Find the angle between the following pair of lines: vecr = 3hati+hatj-...

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  20. Find the angle between the following pair of lines: (x-2)/2=(y-1)/5=(z...

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