Final answer:
The direction of the vector with components Bx = -1.33m and By = 2.81m is found by calculating the arctan of By/Bx and considering the signs of Bx and By to ensure the angle is in the correct quadrant. Therefore, the direction of the vector is approximately 116.67° and represents east in navigational terms.
Step-by-step explanation:
To find the direction of the vector with components Bx = -1.33m and By = 2.81m, we must calculate the vector's angle of direction. The angle θ can be determined using trigonometry, specifically the tangent function, which relates the opposite side (By) to the adjacent side (Bx) of a right triangle: θ = arctan(By/Bx). Substituting the given values and taking the arctan leads us to the angle in radians or degrees, depending on the calculator settings.
To find the direction of the vector, we need to use the given components Bx = -1.33m and By = 2.81m. We can use the tangent function to calculate the angle of the vector. The angle (θ) can be found using the equation tan(θ) = By/Bx. Plugging in the values, we have tan(θ) = 2.81 / -1.33. Calculating this gives us θ ≈ -63.33°. Since the vector is in the second quadrant, we add 180° to the angle to get the actual direction. Therefore, the direction of the vector is approximately 116.67°.
We must also consider the signs of Bx and By to determine the correct quadrant for the angle. The final answer will give us the direction of the vector relative to the positive x-axis, which typically represents east in navigational terms.