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Find the acute angle between the two str...

Find the acute angle between the two straight lines whose direction cosines are given by `l+m+n=0` and `l^2+m^2-n^2=0`

A

`pi/6`

B

`pi/4`

C

`pi/3`

D

`pi/2`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Eliminating n we have `(l^(2)+m^(2))-(l+m)^(2)=0`
`therefore 2lm=0`
When l=0 then m+n=0
`therefore l/0=m/1=n/-1`………(1)
When m=0 then `l+n=0`
`therefore l/1=m/0=n/-1` ………(2)
`therefore` D.R's are 0,1,-1 and 1,0,-1
`therefore costheta=(0.1+1.0+1)/(sqrt(1+1)sqrt(1+1))=1/2`
`therefore=pi/3`
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