The equation of a plane which cuts equal intercepts of unit length on the axes ,is
x+y+z = 0
x+y+z = 1
x+y-z = 0
x/a + y/a + z/a = 1
The direction cosines a line are ( 1/c, 1/c, 1/c) then:
C > 0
0 < C < 1
C ± √3
C > 2
If cos α, cos β, cos γ are the direction cosines of a line, the vale of sin2 α + sin2 β + sin2 γ is
1
2
3
4
The direction cosines of any normal to the XY-plane are
(1,0,0)
(0,1,0)
(1,1,0)
(0,0,1)
If α ,β, γ are the angles which a half ray makes with the positive directions of the axes , then
sin2α + sin2β + sin2γ =
-1
0
If the direction ratios of a line are 1,-3,2 ;then its direction cosines are
1/√14 , -3/√14 ,2/√14
1/√14 , 2/√14 , 3/√14
-1/√14 , 3/√14 , -2/√14
-1/√14 , -2/√14 , -3/√14
The distance of the point ( 2, 3, - 5 ) from the plane x + 2y - 2z = 9 is
The cosine of the angle between any two diagonals of a cube
1/3
1/2
2/3
1/√3
The point which divides the line joining the points (2,4,5) and (3,5,-4) in the ratio -2:3 lies on
ZOX-plane
XOY-plane
YOZ-plane
None of these
The co - ordinates of a points p are ( 3, 12, 4 ) w. r. t. the origin 0. then the direction cosines of OP are:
( 3, 1, 2, 4 )
( 1/4, 1/3, 1/2 )
( 3/13, 12/13, 4/13 )
