Let `alpha, beta, gamma` be distinct real numbers. The points with position vectors `alpha hati + beta hatj +gamma hat k , beta hati + gamma hatj +alpha hat k , gamma hati +alpha hatj + beta hatk`

Options

A. are collinear
B. form an equilateral triangle
C. form a scalene triangle
D. form a right angled triangle

Explanation

To solve the problem, we need to analyze the position vectors given and determine the relationship between the points represented by these vectors. Let's denote the three points as follows:

1. Point A with position vector \( \vec{A} = \alpha \hat{i} + \beta \hat{j} + \gamma \hat{k} \)
2. Point B with position vector \( \vec{B} = \beta \hat{i} + \gamma \hat{j} + \alpha \hat{k} \)
3. Point C with position vector \( \vec{C} = \gamma \hat{i} + \alpha \hat{j} + \beta \hat{k} \)

### Step 1: Check for Collinearity

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