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Prove that the point A(1,2,3), B(-2,3,5)...

Prove that the point `A(1,2,3), B(-2,3,5)` and `C(7,0,-1)` are collinear.

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Using section formula, prove that the points A(-2, 3, 5), B(1,2,3) and C(7,0, -1) are collinear.

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i. Prove that the points vec a-2vec b+3vec c, 2vec a+3vec b-4vec c and -7vecb+10 vec c are are collinear, where vec a, vec b, vec c are non-coplanar. ii. Prove that the points A(1,2,3), B(3,4,7), and C(-3,-2,-5) are collinear. find the ratio in which point C divides AB.

Using the section formula,prove that the three pints A(-2,3,5),B(1,2,3) and C(7,0,-1) are collinear.

(i) Using section formula, show that the points A(-2, 3,5), B(1,2,3) and C(7,0,-1) are collinear. (ii) Using division formula, prove that the points (2,3,4),(-1,-2,1) and (5,8,7) are collinear.

Show that the points A(2,1,3) ,B(5,0,5) and C(-4,3,-1) are collinear .

Show that the points A(1,3,2),B(-2,0,1) and C(4,6,3) are collinear.

i. Prove that the points veca - 2vecb + 3 vecc, 2 veca + 3vecb- 4 vecc and -7 vecb + 10 vecc are collinear, where veca, vec b and vecc are non-coplanar. ii. Prove that the points A(1, 2, 3), B(3,4, 7) and C(-3, -2, -5) are collinear. Find the ratio in which point C divides AB.

NAGEEN PRAKASHAN-THREE-DIMENSIONAL GEOMETRY -Exercise 11 B
  1. Prove that the points A(2,0,-3), B (1,-2,-5) and C(3,2,-1) are colline...

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  2. Prove that the points A(9,-1,4),B(-1,-3,2) and C(4,-2,3) are collinear...

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  3. Prove that the point A(1,2,3), B(-2,3,5) and C(7,0,-1) are collinear.

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  4. Find the values of lambda ad mu if the points A(-1,4,-2),B(lambda,mu,1...

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  5. Find the equation of a line passes through the point hati+hatj+5hatk a...

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  6. The cartesian equation of a line is 6x+1=3y-2 = 3-2x. Find its directi...

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  7. Find the angle between the following pairs of lines (i) veci=3hati+2...

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  8. (i) Show that the line (x+3)/(2) = (y+1)/(-1) = (z+3)/(3) and (x)/(5) ...

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  9. Find the values of lambda if the following of lines perpendicular : ...

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  10. Show that the following pairs of lines intersect. Also find their poin...

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  11. Show that the lines (x-1)/(1) = (y-2)/(-1) = (z-1)/(1) and (x-1)/(1-...

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  12. Show that the lines vecr= hati+hatj-hatk+lambda(3hati-hatj) and vecr =...

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  13. Find the co-ordinates of that point at which the lines joining the poi...

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  14. Find the co-ordinates of that point at which the line joining the poin...

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  15. Find the co-ordinates of a point at which the line (x+1)/(2) = (y-3)/(...

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  16. Find the co-ordinates of a point at which the line (x+1)/(2) = (y-1)/(...

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  17. Find the co-ordiantes of the foot of perpendicular drawn from the poi...

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  18. Find the length and the foot of the perpendicular drawn from the point...

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  19. Find the co-ordinates of the foot of perpendicular and length of perp...

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  20. Find the image of the point (1,6,3) in the line x/1=(y-1)/2=(z-2)/3

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