Solve the problem.
-A ship leaves point $A$ and travels directly north to point $B$. From point $B$, the ship then travels due east to point $C$. The magnitude of the vector from point $A$ to point $C$ is 134 . Find the magnitude of the northern vector. Find the magnitude of the eastern vector.
A) $67 \sqrt { 2 }$ north; $67 \sqrt { 2 }$ east
B) 67 north; $67 \sqrt { 3 }$ east
C) 67 north; 67 east
D) $67 \sqrt { 3 }$ north; 67 east

Question

Quizplus · Accepted Answer

The vector from A to C forms a right-angled triangle with the north and east vectors as the legs. Since the magnitude of the vector from A to C is 134, and it forms a 45-degree angle (implied by the equal magnitudes of the north and east vectors), the north and east vectors must each have a magnitude of $67 \sqrt { 2 }$.

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