a boat is traveling at a speed of 50 kilometers per hour, in a direction that is $45^{\\circ}$ to the west…

a boat is traveling at a speed of 50 kilometers per hour, in a direction that is $45^{\\circ}$ to the west from the northward direction.\n\nhere are a few vectors, where $||\\vec{a}|| = ||\\vec{b}|| = ||\\vec{c}|| = ||\\vec{d}|| = 50 \\frac{\\text{km}}{\\text{h}}$\n\nwhich vectors can represent the boats velocity?\nchoose all answers that apply:\na $\\vec{a}$\nb $\\vec{b}$\nc $\\vec{c}$\nd $\\vec{d}$

a boat is traveling at a speed of 50 kilometers per hour, in a direction that is $45^{\\circ}$ to the west from the northward direction.\n\nhere are a few vectors, where $||\\vec{a}|| = ||\\vec{b}|| = ||\\vec{c}|| = ||\\vec{d}|| = 50 \\frac{\\text{km}}{\\text{h}}$\n\nwhich vectors can represent the boats velocity?\nchoose all answers that apply:\na $\\vec{a}$\nb $\\vec{b}$\nc $\\vec{c}$\nd $\\vec{d}$

Answer

Brief Explanations:

First, define the direction: 45° west from northeast means the vector points 45° toward the west axis relative to the northeast (north-east) direction, which is equivalent to a direction that is northwest-angled 45° from north, matching vector $\vec{a}$. The magnitude of $\vec{a}$ is also $50 \frac{\text{km}}{\text{h}}$, which matches the boat's speed.

Answer:

A. $\vec{a}$