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Prove that the straight lines whose dire...

Prove that the straight lines whose direction cosines are given by `a^(2)l+b^(2)m+c^(2)n=0` and `mn+nl+lm=0` are parallel if `a+b+c=0`.

Answer

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Prove that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and fmn+gnl+hlm=0 are parallel if a^(2)f^(2)+b^(2)g^(2)+c^(2)h^(2)-2(abfg+bcgh+cahf)=0

Prove that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and fmn+gnl+hlm=0 are at right angles if f/a+g/b+h/c=0

Knowledge Check

  • The angle between the pair of straight lines whose direction cosines are given by the equations 2l-m+2n=0 and mn+nl+lm=0 is -

    A
    `(pi)/(2)`
    B
    `(pi)/(4)`
    C
    `(pi)/(3)`
    D
    `(pi)/(6)`

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    Show that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and u l^2+v m^2+w n^2=0 are parallel or perpendicular as a^2/u+b^2/v+c^2/w=0 or a^2(v +w)+b^2(w+u)+c^2(u+v)=0

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    Show that the pair of staright lines whose direction cosines are given by al+bm+cn=0 and pl^(2)+qm^(2)+rn^(2)=0 are perpendicular to each other if a^(2)(q+r)+b^(2)(r+p)+c^(2)(p+q) =0

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