Relative to the origin $O$, the position vectors of two points $A$ and $B$ are $\mathbf{a}$

Question

Relative to the origin $O$, the position vectors of two points $A$ and $B$ are $\mathbf{a}$ and $\mathbf{b}$ respectively. The length of $\mathbf{a}$ is $k$ units and $\mathbf{b}$ is a unit vector. The angle between $\mathbf{a}$ and $\mathbf{b}$ is $\frac{\pi}{6}$ radians. It is given that the point $M$ lies on the line segment $AB$ such that $AM:AB$ is $3:4$, find exact area of $\Delta OAM$, giving your answer in terms of $k$.[4]

Accepted Answer

Area of $\triangle OAM = \frac{3}{16}k\,\mathrm units^2$

2025 ASRJC P2 Q1

2025 ASRJC P2 Q1