Question

The acute angle between the lines whose direction cosines are given

Answer 1

Step-by-step explanation:

Toolbox:

Angle between two lines is cosθ=b1→.b2→|b1→||b2→|

Step 1:

Given that l+m+n=0 -----(1)=>l+m=−n

=>−(l+m)=n

and l2+m2−n2=0-----(2)

Let us substitute for ′n′ in equation (2) we get

=>l2+m2−l2−m2−2ml=0

or 2ml=0

(ie) either l=0orm=0

Let us put m=0 in equation (1)

If m=0 then l=−n

direction ratios (l,m,n)=(1,0,−1)

Let us put l=0 we get m=−n

direction ratios (l,m,n)=(0,1,−1)

Step 2:

Let us find out b1.b2

b1.b2=(1,0,−1).(0,1,−1)

=0+0+1

1

|b1|=02+12+(−1)2−−−−−−−−−−−−−√=2–√

|b2|=02+12+(−1)2−−−−−−−−−−−−−√=2–√

Step 3:

Now substituting the above values in

cosθ=b1→.b2→|b1→||b2→|

cosθ=12–√2–√=12

=>θ=π3