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Prove that the straight lines whose dire...

Prove that the straight lines whose direction cosines are given by the relations `al+bm+cn=0 and fmn+gnl+hlm=0` are
Perpendicular to each other if `(f)/(a)+(g)/(b)+(h)/(c)=0`, and
parallel if `a^(2)f^(2)+b^(2)g^(2)+c^(2)h^(2)-2bcgh-2cahf-2abfg=0`.

A

`sqrt(af)+sqrt(bg)+sqrt(ch)=0`

B

`a^(2)/f+b^(2)/g+c^(2)/n=0`

C

`f/a+g/b+h/c=0`

D

`a^(2)f^(2)+b^(2)g^(2)+c^(2)h^(2)-2bcgh-2cahf-2abfg=0`

Text Solution

Verified by Experts

The correct Answer is:
C
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