A particle is moving with velocity ` vecv = k( y hat(i) + x hat(j)) `, where `k` is a constant . The genergal equation for its path is

Options

A. ` y = x ^ 2 ` + constant
B. `y ^ 2 = x + ` constant
C. `xy ` = constant
D. ` y ^ 2 = x ^ 2 + ` constant

Explanation

To solve the problem, we need to find the general equation for the path of a particle moving with the given velocity vector. Let's break down the solution step by step.

### Step 1: Write the velocity vector
The velocity vector is given as:
\[ \vec{v} = k(\hat{y} + \hat{x}) \]
This can be rewritten in component form:
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