Question

Given three displacement vectors b,c,and d such that b =(-i 2j )m, c =(3i -2j )m and d of unknown components, determine the magnitude and direction of d for 3b - c d = 0

Answer 1

To find the magnitude and direction of vector d, we can use the given equation 3b - c + d = 0. Substituting the given values for b and c, we get d = 6i - 7j m. The magnitude of d is sqrt(85) and its direction is approximately -47.81° relative to the positive x-axis.

Step-by-step explanation:

To find the magnitude and direction of vector d, we can use the given equation 3b - c + d = 0. Rearranging the equation, we have d = c - 3b. Substituting the given values for b and c, we get d = (3i - 2j)m - 3(-i + 2j)m = 6i - 7j m.

So, the magnitude of d is sqrt(6^2 + (-7)^2) = sqrt(36 + 49) = sqrt(85).

As for the direction, we can use the inverse tangent function to determine the angle. The direction angle of d is tan^(-1)(-7/6) ≈ -47.81°. Therefore, the magnitude of vector d is sqrt(85) and its direction is approximately -47.81° relative to the positive x-axis.