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Show that the plane a x+b y+c z+d=0 divi...

Show that the plane `a x+b y+c z+d=0` divides the line joining the points `(x_1, y_1, z_1)a n d(x_2, y_2, z_2)` in the ratio `(a x_1+b y_1+c z_1+d)/(a x_2+b y_2+c z_2+d)` .

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Show that the plane ax+by+cz+d=0 divides the line joining the points (x_(1),y_(1),z_(1)) and (x_(2),y_(2),z_(2)) in the ratio (ax_(1)+by_(1)+cz_(1)+d)/(ax_(2)+by_(2)+cz_(2)+d)

Show that the plane ax+by+cz+d=0 divides the line joining (x_1, y_1, z_1) and (x_2, y_2, z_2) in the ratio of (-(ax_1+ay_1+cz_1+d)/(ax_2+by_2+cz_2+d))

XY - plane divides the line joining A(x_(1),y_(1),z_(1)) and B(x_(2),y_(2),z_(2)) in the ratio

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The equation of the plane containing the line 2x+z-4=0 nd 2y+z=0 and passing through the point (2,1,-1) is (A) x+y-z=4 (B) x-y-z=2 (C) x+y+z+2=0 (D) x+y+z=2

The equation of the plane containing the line 2x+z-4=0 nd 2y+z=0 and passing through the point (2,1,-1) is (A) x+y-z=4 (B) x-y-z=2 (C) x+y+z+2=0 (D) x+y+z=2

MODERN PUBLICATION-STRAIGHT LINES -Revision exercise
  1. A line is such that its segment between the lines 5x -y+4=0 and 3x +4y...

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  2. Find the distance of the line 4x y = 0from the point P(4, 1) measure...

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  3. Show that the plane a x+b y+c z+d=0 divides the line joining the point...

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  4. Prove that (-1,4) is the orthocentre of the triangle formed by the lin...

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  5. The equation of the perpendicular bisector of the side AB of a triangl...

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  6. The opposite angular points of a square are (3,4) a) and (1,-1). Then ...

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  7. Using the concept of slope, prove that medians of an equilateral tr...

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  8. Show that the perpendicular drawn from the point (4,1) on the line seg...

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  9. A rectangle has two opposite vertices at the points (1,2)a n d(5,5)dot...

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  10. Find the coordinates of the incentre and centroid of the triangle whos...

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  11. The vertices of a triangle are A(x1, x1tantheta1),B(x2, x2tantheta2)a ...

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  12. The points (1, 3) and (5, 1) are two opposite vert of a rectangle. Th...

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  13. One side of a rectangle lies along the line 4x+7y+5=0. Two of its vert...

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  14. Two consecutive sides of a parallelogram are 4x+5y=0 and 7x+2y=0 . If ...

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  15. One side of a square is inclined to the x-axis at an angle alpha and o...

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  16. On the portion of the line x+3y-3=0 which is intercepted between the c...

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  17. Find the direction in which a straight line must be drawn through the...

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  18. The hypotenuse of a right angled isosceles triangle has its ends at th...

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  19. A ray of light passing through the point (1,2) reflects on the x-a xi ...

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  20. A person standing at the junction (crossing) of two straight paths rep...

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