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If `r_(1),r_(2) and r_(3)` are the position vectors of three collinear points and scalars `l` and `m` exists such that `r_(3)=lr_(1)+mr_(2)`, then show that `l+m=1`.

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To solve the problem, we need to show that if \( r_1, r_2, \) and \( r_3 \) are the position vectors of three collinear points and scalars \( l \) and \( m \) exist such that \( r_3 = l r_1 + m r_2 \), then \( l + m = 1 \). ### Step-by-Step Solution: 1. **Understanding Collinearity**: Since \( r_1, r_2, \) and \( r_3 \) are position vectors of collinear points, we can express the vector \( r_3 \) in terms of \( r_1 \) and \( r_2 \). 2. **Defining Vectors**: ...
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