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If l , m,n are three lines such that l...

If `l , m,n` are three lines such that `l |\| m` and `n_|_l ,` prove that `n_|_mdot`

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To prove that line \( n \) is perpendicular to line \( m \) given that line \( l \) is parallel to line \( m \) and line \( n \) is perpendicular to line \( l \), we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Given Information**: - We have three lines: \( l \), \( m \), and \( n \). - It is given that \( l \parallel m \) (lines \( l \) and \( m \) are parallel). - It is also given that \( n \perp l \) (line \( n \) is perpendicular to line \( l \)). ...
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Knowledge Check

  • If l , m, n are the direction consines of a line, then

    A
    `l+m+n=0`
    B
    `l+m+n=1`
    C
    `l^(2)+m^(2)+n^(2)=1`
    D
    `l^(2)+m^(2)+n^(2)=0`

  • If l,m,n are direction cosines of the line then -l,-m,-n can be

    A
    only direction ratios of the line
    B
    only direction cosines of the line
    C
    direction cosines and direction ratios of the line
    D
    neither direction cosines nor direction ratios of the line

  • If l, m, n are direction cosines of a line then l hat(i) + m hat(j) + n hat(k) is________

    A
    Null vector
    B
    the unit vector along the line.
    C
    Any vector along the line
    D
    a vector perpendicular to the line

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    Two lines l and m interset at the O and P is Point on a line n Passing through the point O such that P is equidistant from l and m. Prove that n is the bisectof the angle formed by l and m

    In a A B C , If L a n d M are points on A B a n d A C respectively such that L M B Cdot Prove that: a r ( A B M)=a r ( A C L)

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    If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are the direction cosines of two lines and l , m, n are the direction cosines of a line perpendicular to the given two lines, then

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