If a line lies in the octant OXYZ and it makes equal angles with the axes ,then
l=m=n=1/√3
l=m=n=±1/√3
l=m=n=-1/√3
l=m=n=±1/√2
The equation of the plane passing through (2,3,4) and parallel to the plane 5x-6y+7z=3 is
5x-6y+7z+20 = 0
5x-6y+7z-20=0
-5x+6y-7z+3=0
5x+6y+2z+3=0
The projection of the line joining the points (3,4,5) and (4,6,3) on the line joining the points (-1,2,4) and (1,0,5) is :
4/3
2/3
-4/3
1/2
A variable plane moves ,so that the sum of the reciprocals of its intercepts on the co-ordinate axes is 1/2.Then the plane passes through .
(1/2,1/2,1/2)
(-1,1,1)
(2,2,2)
(0,0,0)
The equation to the straight line passing through the points (4,-5,-2) and (-1,5,3) is
x-4/1=y+5/-2=z+2/-1
x+4/1=y-5/2=z-3/-1
x/-1=y/5=z/3
x/4=y/-5=z/-2
The plane x/2 + y/3 + z/4 = 1,cut the axes in A,B,C then the area of the Δ ABC is
√29 Sq - unit
√41 Sq - unit
√61 Sq - unit
None of these
The points A (4,5,1), B (0,-1,-1) (3,9,4) and D (-4,4,4) are:
Collinear
Coplanar
Non - coplanar
non collinear and non coplanar
The direction cosines of the line joining the points (4,3,-5) and (-2,1,-8) are
(6/7 , 2/7 , 3/7 )
(2/7 , 3/7 , 6/7 )
(6/7 , 3/7 , 2/7 )
The xy-plane divides the line joining the points (-1,3,4) and (2,-5,6)
internally in the ratio 2 : 3
externally in the ratio 2 : 3
internally in the ratio 3 : 2
externally in the ratio 3 : 2
If the plane x+2y+2z-15=0 cuts the circle x2 + y2 + z2 - 2y-4z-11=0,then radius of circle is
√3
√5
√7
3
