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1. Find the direction cosines of a line which makes an angle with all three the coordinate axes.
A. ± 1/√2
B. 1/√3
C. 1/√2
D. ± 1/√3
2. Three planes, viz the XY Plane, XZ Plane and the YZ Plane divide the space into eight parts. Each part is called an OCTANT. What is the relation between these three planes
A. They form the angles α, β & γ with each other
B. Any two must be perpendicular to each other.
C. All three are mutually perpendicular
D. no relation between these three planes
3. The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:
A. 1 , 0 , -2/3
B. 3/√13, 0, -2/√13
C. 3/4, 0, -2/4
D. -3/√12, 0, -2/√13
5. The direction cosines of the line equally inclined with the axes are:
A. 1, 1, 1
B. 1/√3, 1/√3, 1/√3
C. 1, 0, 0
D. 1/3, 1/3, 1/3
7. Find the direction cosines of the x axis.
A. 1, 0, 0
B. 0, 0, 0
C. 0, 1, 0
D. 0, 0, 1
9. What are direction numbers of a line.
A. numbers which are proportional to the direction cosines of a line
B. numbers which are proportional to the direction cosines of a line.
C. numbers which are same as direction angles of a line
D. numbers which are proportional to the direction angles of a line
10. What are direction ratios of a line.
A. numbers which are proportional to the direction angles of a line
B. numbers which are proportional to the direction cosines of a line
C. numbers which are same direction angles of a line
D. numbers which are proportional to the direction cosines of a line
12. If l, m , n are the direction cosines of any line, then sum of the squares of the direction cosines of the line is always
A. -1
B. √3
C. 1
D. 0
13. If a line has the direction ratios -4, 18, -12 then what are its direction cosines?
A. -2, 9, -6
B. -4, 18, -12
C. 2/11, 9/11, 6/11
D. -2/11, 9/11, -6/11
14. The direction cosines of the line equally inclined with the axes, are:
A. 1, 1, 1,
B. 0, 0, 0
C. 1/3, 1/3, 1/3
D. 1/√3, 1/√3, 1/√3
16. Find the equation of the set of points which are equidistant from the points (1, 2 , 3) and (3, 2, -1)
A. x + 2z = 0
B. y + 2z = 0
C. x - 2y = 0
D. x - 2z = 0
19. The signs of the X,Y and Z coordinates of a point that lies in the octant OXYZ' is
A. (- , + , +)
B. (-, - , +)
C. ( + , - , -)
D. ( + , + , -)
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