A hiker walks from a campsite at to a waterfall at

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

A hiker walks from a campsite at

C_1(−2\,\text{km},\,1\,\text{km})

to a waterfall at

C_2(3\,\text{km},\,4\,\text{km})

, and then proceeds to a viewpoint at

C_3(7\,\text{km},\,−1\,\text{km})

. (a) Determine the displacement vector for each leg of the journey, namely

\overrightarrow{C_1C_2}

and

\overrightarrow{C_2C_3}

. (b) Using your results from part (a), find the net displacement vector

\overrightarrow{C_1C_3}

in component form. (c) Verify, by explicit calculation, that the vector sum

\overrightarrow{C_1C_2}+\overrightarrow{C_2C_3}

equals

\overrightarrow{C_1C_3}

. (d) Calculate the magnitudes of

\overrightarrow{C_1C_2}

\overrightarrow{C_2C_3}

, and

\overrightarrow{C_1C_3}

, and comment on the relationship between the algebraic sum of the first two magnitudes and the magnitude of the net displacement.