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Two friends are planning a road trip. One friend stays in City A represented by the position vector…
Two friends are planning a road trip. One friend stays in City A represented by the position vector $(-2\hat{i} + 3\hat{j} + 5\hat{k})$. The trip will start from City A and proceed towards the City B represented by the position vector $(\hat{i} + 2\hat{j} + 3\hat{k})$. The friend living in City C represented by the position vector $7\hat{i} - \hat{k}$ will join when the first friend passes through her city.
(a)
Find the vector equation for the straight path between the cities A and B.
(b)
Hence, find out whether the three cities lie on the same straight path.
(c)
If the two friends now plan to travel $\sqrt{126}$ units along the vector $\vec{AB}$ from the City C, find the position vector of the destination point.
Answer
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From ISC 2025 Practice Mathematics, question 111.