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If r(1),r(2) and r(3) are the position v...

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 prove that \( l + m = 1 \) given that \( \mathbf{r}_3 = l \mathbf{r}_1 + m \mathbf{r}_2 \) for three collinear points represented by their position vectors \( \mathbf{r}_1, \mathbf{r}_2, \) and \( \mathbf{r}_3 \), we can follow these steps: ### Step 1: Understand the relationship between the vectors Since the points represented by the vectors \( \mathbf{r}_1, \mathbf{r}_2, \) and \( \mathbf{r}_3 \) are collinear, we can express the position vector of one point as a linear combination of the other two. ### Step 2: Set up the equation We know that: \[ ...
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