- Final answer:
The magnitude of vector -3w is three times the magnitude of vector w but in the opposite direction. Components of w can be found using trigonometry, multiplying the magnitude of w by the cosine or sine of its angle.
Step-by-step explanation:
The magnitude of vector -3w would be three times the magnitude of vector w. Since the vector is multiplied by a negative scalar, it will be in the opposite direction of w, but it will still have the same magnitude, only multiplied by three.
Components of vector w can be found using trigonometric principles. For instance, if vector w has a magnitude and a direction, its components can be calculated by multiplying the magnitude of w by the cosine of the angle for the x-component and by the sine of the angle for the y-component.
This is shown in the equation W1 = w cos(0) = mg cos(0), which describes the x-component of the weight vector on an incline.
When resolving vectors into their scalar components such as Ex, Ey, and Ez, trigonometry and geometrical understanding of the vectors and angles can be applied.
The complete question is: Which components are a possible representation of vector w if the magnitude of vector -3w is ||-3w||=15?<1,-9>