Direction Cosines And Direction Ratios Of A Line

Question 1

if a directed line L passing through the origin makes angles a, b and g with x, y and z-axes, respectively, called direction angles then

Answer 1

cosine
of these angles, namely, cos a, cos b and cos g are called direction cosines of the
directedline L.

Question 2

If we reverse the direction of L by 180° then

Answer 2

Direction cosines are pi-a,pi-b,pi-g

Question 3

Numbers which are proportional to the direction cosines of a line are called

Answer 3

Direction ratios a,b,c

Question 4

If direction cosines cos a=l cos b=m cos g=n and direction ratios a,b,c then

Answer 4

a=ñl b=ñm c=ñn

Question 5

If l,m,n are direction cosines and a,b,c are direction ratios then

Answer 5

l/a=m/b=n/c=k(constant)
k=+_l/sqrt a^2+b^2+c^2

Question 6

dc’s of a line are

Answer 6

l=+_a/sqrt a^2+b^2+c^2
m=+_b/sqrt a^2+b^2+c^2
n=+_c/sqrt a^2+b^2+c^2

Question 7

For any line there are infinitely many

Answer 7

Sets of direction ratios

Question 8

any two sets of direction ratios of a line are also

Answer 8

Proportional

For any line, if a, b, c are direction ratios of a line, then ka, kb, kc; k ≠ 0 is also a set of direction ratios.