Vector Algebra
Section Formula
Grade 12
Question:
<p>In a triangle AOB, R and Q are the points on the side OB and AB respectively such that <span>\(3OR = 2RB\)</span> and <span>\(2AQ = 3QB\)</span>. Let OQ and AR intersect at the point P (where O is origin). If the point P divides OQ in the ratio of m:1, then m is:</p>
<p>(a) <span>\frac{2}{19}</span></p>
<p>(b) <span>\frac{2}{17}</span></p>
<p>(c) <span>\frac{2}{15}</span></p>
<p>(d) <span>\frac{10}{9}</span></p>
Step-by-Step Solution
Key Concept: Use position vectors and the condition that P lies on both OQ and AR to set up equations and solve for the ratio.
Using section formula and vector algebra, we find the position of P on OQ. The point P divides OQ in ratio m:1 where m = \frac{10}{9} .
Correct Answer: d