JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(O\) be the origin, \(\vec{OP} = \vec{a}\) and \(\vec{OQ} = \vec{b}\). If \(R\) is the point on \(\vec{OP}\) such that \(\vec{OP} = 5\vec{OR}\), and \(M\) is the point such that \(\vec{OQ} = 5\vec{RM}\), then \(\vec{PM}\) is equal to :
- A \(\dfrac{1}{5}(\vec{a} - 4\vec{b})\)
- B \(\dfrac{1}{5}(\vec{b} - 4\vec{a})\)
- C \(\dfrac{1}{5}(-\vec{a} + 4\vec{b})\)
- D \(\dfrac{1}{5}(-\vec{b} + 4\vec{a})\)
Answer & Solution
Correct Answer
(B) \(\dfrac{1}{5}(\vec{b} - 4\vec{a})\)
Step-by-step Solution
Detailed explanation
Given \(\vec{OP} = \vec{a}\) and \(\vec{OQ} = \vec{b}\). Since \(\vec{OP} = 5\vec{OR}\), we have \(\vec{OR} = \dfrac{\vec{a}}{5}\). Also, \(\vec{OQ} = 5\vec{RM}\), which gives \(\vec{RM} = \dfrac{\vec{b}}{5}\). The position vector of \(M\) is given by…
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