MHT CET · Maths · Vector Algebra
If \(\vec{a}, \vec{b}, \vec{c}\) are position vectors of points \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) respectively, with \(2 \vec{a}+3 \vec{b}-5 \vec{c}=\overrightarrow{0}\), then the ratio in which point \(\mathrm{C}\) divides segment \(\mathrm{AB}\) is
- A 2:3 internally
- B 2:3 externally
- C 3:2 internally
- D 3:2 externally
Answer & Solution
Correct Answer
(C) 3:2 internally
Step-by-step Solution
Detailed explanation
\(2 \vec{a}+3 \vec{b}=5 \vec{c} \Rightarrow \vec{c}=\frac{2 \vec{a}+3 \vec{b}}{5}=\frac{2 \vec{a}+3 \vec{b}}{2+3}\)
i.e., \(\vec{c}\) divides \(\vec{a}\) and \(\vec{b}\) in the ratio 3:2 internally
i.e., \(\vec{c}\) divides \(\vec{a}\) and \(\vec{b}\) in the ratio 3:2 internally
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