Final answer:
To write a given vector in terms of i and j, we need to find the components of the vector along the x-axis (i) and the y-axis (j). The component of the force vector G along the force vector = (1.01 + 4.0j) N is 12.305 N.
Step-by-step explanation:
To write a given vector in terms of i and j, we need to find the components of the vector along the x-axis (i) and the y-axis (j). Let's consider the vector G = (3.01 + 4.0j + 10.0k) N and the force vector = (1.01 + 4.0j) N.
To find the component of vector G along the force vector, we take their dot product. The dot product of two vectors is given by G ⋅ = Gx x + Gy y, where Gx and Gy are the components of G along the x and y axes, respectively. In this case, Gx = 3.01 N and Gy = 4.0 N. Thus, the component of G along the force vector is obtained by multiplying the magnitude of the force vector with the cosine of the angle between the two vectors.
Let's calculate the dot product: G ⋅ = (3.01)(1.01) + (4.0)(4.0) = 12.305 N. Therefore, the component of the force vector G along the force vector = (1.01 + 4.0j) N is 12.305 N.