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Standard XII

Physics

Position Vector

If a⃗ and ...

Question

If $\to a$ and $\to b$ are position vectors of point s A and B respectively, then the position vector of points of trisection of AB

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Solution

Let P and Q be the point of trisection of AB, i.e. AP=PQ=QB
Since, point P divides AB in the ratio $1 : 2$
Therefore the position vector of P=
$\frac{1 \cdot \to b + 2 \to a}{1 + 2} = \frac{2 \to a + \to b}{3}$
Since, point Qdivides AB in the ratio $2 : 1$
Therefore the position vector of Q=
$\frac{2 \cdot \to b + 1 \cdot \to a}{1 + 2} = \frac{\to a + 2 \to b}{3}$

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Similar questions

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If →a and →b are position vectors of point s A and B respectively, then the position vector of points of trisection of AB

Let P and Q be the point of trisection of AB, i.e. AP=PQ=QBSince, point P divides AB in the ratio 1:2Therefore the position vector of P=1⋅→b+2→a1+2=2→a+→b3Since, point Qdivides AB in the ratio 2:1Therefore the position vector of Q=2⋅→b+1⋅→a1+2=→a+2→b3

If $\to a$ and $\to b$ are position vectors of point s A and B respectively, then the position vector of points of trisection of AB