Vector {\bf{\vec V}}_1 is 6.3 units long and points along the negative x axis. Vector {\bf{\vec V}}_2 is 8.5 units long and points at 30^\circ to the positive x axis.
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To find the components of vector V1, we need to consider its magnitude (length) and the direction it points. We know that vector V1 has a length of 6.3 units and points along the negative x-axis.
The negative x-axis means that the x-component of vector V1 is negative, while the y-component is zero. Therefore, we can write vector V1 as:
V1 = (-6.3, 0)
Similarly, to find the components of vector V2, we need to consider its magnitude and the angle it makes with the positive x-axis. We know that vector V2 has a length of 8.5 units and points at an angle of 30 degrees with respect to the positive x-axis.
To find the x- and y-components of vector V2, we can use the following trigonometric relationships:
x-component = length * cosine(angle)
y-component = length * sine(angle)
Plugging in the values we have:
x-component = 8.5 * cos(30) ≈ 7.358 units
y-component = 8.5 * sin(30) ≈ 4.25 units
Therefore, the components of vector V2 can be written as:
V2 = (7.358, 4.25)