Point S divides PQ in the ratio 5:2. Express OS in terms of p and q.

April 15, 2026Mathematics

ScanSolve AI Answer

April 15, 2026

Answer

\frac{5}{7}\vec{PQ}$.

a) Express in terms of $\mathbf{p}$ and $\mathbf{q}$ .

i) $\vec{OS}$ Point S divides PQ in the ratio 5:2. This means $\vec{PS} = \frac{5}{7}\vec{PQ}$ . First, find $\vec{PQ}$ : $\vec{PQ} = \vec{OQ} - \vec{OP} = q - p$ Now, find $\vec{OS}$ : $\vec{OS} = \vec{OP} + \vec{PS}$

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a) Express in terms of p and q. i) OS Point S divides PQ in the ratio 5:2.

Asked on April 15, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 15, 2026

a) Express in terms of p and q. i) OS Point S divides PQ in the ratio 5:2. This means PS = (5)/(7)PQ. First, find PQ: PQ = OQ - OP = q - p Now, find OS: OS = OP + PS OS = p + (5)/(7)(q - p