Find the coordinates of the vector 1/3 a + b if a {0, 3, -6} b {5, -2, 1}

To calculate the coordinates of the desired vector (1/3 * a ̅ + b ̅), let’s first find the coordinates of the vector c ̅ = 1/3 * a ̅. This can be done by multiplying the coordinates of the vector a ̅ by 1/3:

c ̅ = {0/3, 3/3, -6/3} = {0, 1, -2}

Then, the coordinates of the vector (1/3 * a ̅ + b ̅) are calculated by adding the coordinates of the vector c ̅ with the coordinates of the vector b ̅:

1/3 * a ̅ + b ̅ = c ̅ + b ̅ = {0 + 5, 1 + (-2), (-2) + 1} = {5, -1, -1}

Answer: the required coordinates {5, -1, -1}