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The position vectors of two points A and...

The position vectors of two points A and B are `3hati+hatj+2hatk and hati-2hatj-4hatk`, respectively. Find the equation of the plane passing through B and prependicular to AB.

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Find the vector projection of veca=hati-hatj+hatk on vecb=3hati+hatj+3hatk.

Find the area of the parallelogram whose diagonals are vectors 3hati+hatj-2hatk and hati-3hatj+4hatk .

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SHARAM PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXAMPLE
  1. Find the equation of the line through the point (2, 3, 5) and parallel...

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

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

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

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

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

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

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

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

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

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

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

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  14. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

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  15. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  16. Prove that the measure of the angle between two main diagonals of a cu...

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  17. If P (1,y,z) lies on the line through (3,2,-1) and (-4,6,3) find y & z...

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  18. Find the equation of the plane passing through the foot of the perpend...

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  19. Find the equation of the plane passing through the points (2, 1, -1) a...

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  20. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

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