A golf takes three putts to get the ball into the hole. The first putt displaces the ball `3.66` m north, the second `1.83` m southeast, and the thirs `0.91` m southwest. What are (a) the magnitude and (b) the direction of the displacement needed to get the ball into the hole on the first putt ?

Explanation

To solve the problem step by step, we will break down the displacements into their vector components and then find the resultant vector that represents the displacement needed to get the ball into the hole in one putt.

### Step 1: Represent the Displacements as Vectors
1. **First Putt (A)**: The first putt displaces the ball 3.66 m north. In vector form, this can be represented as:
\[ \vec{A} = 3.66 \hat{j} \]

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