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Direction cosines connected by a linear and a quadratic relation

This type of question, asked 3 times: 11 May 2024 S1, 14 May 2024 S1, 26 Apr 2025 S1. All 3 questions below, oldest first.

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  1. Question 1

    11 May 2024 S1

    111
    If the direction cosines l,m,nl, m, n of two lines are connected by relations l−5m+3n=0l - 5m + 3n = 0 and 7l2+5m2−3n2=07l^2 + 5m^2 - 3n^2 = 0, then value of l+m+nl+m+n is

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  2. Question 2

    14 May 2024 S1

    110
    The angle between the lines, whose direction cosines l,m,nl,m,n satisfy the equations l+m+n=0l+m+n=0 and 2l2+2m2−n2=02l^2+2m^2-n^2=0, is:

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  3. Question 3

    26 Apr 2025 S1

    127
    The angle between lines whose direction cosines satisfy the equation l+m+n=0l+ m + n = 0 and l2−m2−n2=0l^{2}-m^{2}-n^{2}= 0, is

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