Find the angle between the lines whose direction cosines are given by l+m+n=0 and 2l2+2m2−n2=0

Question

Find the angle between the lines whose direction cosines are given by l+m+n=0 and 2l2+2m2−n2=0
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Solution 1

The angle between two lines with direction cosines (l1, m1, n1) and (l2, m2, n2) is given by the formula:

cos θ = l1l2 + m1m2 + n1*n2

Given the direction cosines of the two lines are l+m+n=0 and 2l^2+2m^2−n^2=0, we can express m and n in terms of l for both lines.

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