Assignment-9
Class- Xt ( mathematics)
Straight lines and Three dimensionalGeometry
L' Show that the line joining (-2,6) and (4,8) is perpendicular to the Iine joining (a,t2)
and (4,24).
2.lf the points (a,0), (0,B) and (3,4) are collinear,show that 3/a + 4/b 1
=
3'Find the eguation of the straight line which passes through (3,4) and the
sum of whose intercepts on the coordinates axes is 14.
4. show that (4,4), (3,5) and (-1,-1)are the vertices of a right angre triangre.
5'Determine the equation of the line which cuts off an intercept -s on y-axis
having slope 1/2.
6 Find the equation of the line passing through (-3,5) and perpendicular
to the line through the points (2,5)and (-3,8).
7'Findthe equation of the line passingthrough the intersection of the lines + +
x )/ 1= 0 and
distance from the origin is 1.
x*y+
1=0 and whose
I
\
8. Find the value of p for which the foilowing rines are perpendicurar.
px+3y=4and 3x-4y=
9'Find the equation
(2,3).
l
7
ofa line that cuts offequal intercepts
on the co-ordinates axes and passes through the point
10'Find the equation of the line passing through (3,-2) and inclined at
an angle of 60oto line V3 x + y -1.
1'5how that the three points A (7,-2,-81, 8{5,0,-2) and C(11,3,7) are
collinear. AIso find the ratio in which B divides
AC.
2.Find the ratio in which the line joining the points (-2,4,5) and (3,-5,4)is
divided by yz plane.
3;Using section formula, show that the points (2,-3,4),(-1.,2,1) and (o,L/3,21are
collinear.
4.Find the ratio in which the line segment joining the points A(L,2,3)
and B(-4,5,-2)is divided by the
planex
+2y-z=4
5.centroid of a triangle with vertices (a,!.,3),(-2,b,-.5)and (4,7,c) is origin.Find
the values of a,b,c.
5'Flhd the co ordinates of the points which trisect the line segment joining
the points p( 4,-2,-3)and Q (g,-6,4).
7'Show that the points (4,2,4),(L0,2,-2) and (2,o,-4) are the vertices
of
an equilateral triangle.
8'Show that the points (0,4,!),(2,3,-L),(4,5,o) and (2,6,2)are the vertices
of a square.
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