A car is moving with a speed of `10m s^(-1)`, If the east direction taken as x-axis and the north direction as y-axis . Write the velocity vector of car in unit vector notation.If it is moving (a) in the direction of N-E,(b) in the direction of `N-W`,(C ) in the direction of` S-W`, and (d) in the direction of `S-E`.

Explanation

To solve the problem of determining the velocity vector of a car moving at a speed of \(10 \, \text{m/s}\) in various directions, we will express the velocity vector in unit vector notation for each specified direction. The east direction is taken as the x-axis and the north direction as the y-axis.

### Step-by-Step Solution:

1. **Understanding Unit Vector Notation**:
- The velocity vector can be expressed in the form \( \vec{v} = v_x \hat{i} + v_y \hat{j} \), where \(v_x\) is the component in the x-direction (east) and \(v_y\) is the component in the y-direction (north).

2. **Magnitude of Velocity**:
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