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Show that the point (3, -2, 4), (1, 1, 1...

Show that the point (3, -2, 4), (1, 1, 1) and (-1, 4,-2)are collinear.

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SHARAM PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXAMPLE
  1. Fill in the blanks in the length of the projection of the line segment...

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  2. What are the d.cs of the line through (1,-1, 1)and (2, -5,-3)?

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  3. Show that the point (3, -2, 4), (1, 1, 1) and (-1, 4,-2)are collinear...

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  4. What is the equation of x-axis in symmetric form.

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  5. What are the d.cs of the line x = y = z.

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  6. Write down the d.rs of the line 2x = 3y = 4z.

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  7. Write the equation of the plane passing through the point (3, 1, 2) a...

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  8. Find the equation of the line through the point (2, 3, 5) and parallel...

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  9. Show that lines vecr = (hat(i) + hat(j) - hat(k)) + lambda(3hat(i) - h...

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  10. The position vectors of two points A and B are 3hati+hatj+2hatk and ha...

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  11. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

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  12. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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  13. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  14. Find the shortest distance between the following lines vecr = 2hat(i) ...

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  15. Find the shortest distance between the lines  (x-8)/(3) = (y+9)/(-16) ...

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  16. Find the distance of the point (-1,-5,-10) from the point of intersect...

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  17. The projection of a line segment overline(OP), through origin O, on th...

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  18. passing through the point (-1,3,2) perpendicular to the planes x+2y+...

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  19. Prove that the lines (x+4)/3=(y+6)/5=(z-1)/(-2) and 3x-2y+z+5=0=2x+3y...

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  20. Find the locus of points which are equidistant from the points (1,2,3)...

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