Which of the following statement is true.

Options

A. `vec(a)` and `vec(-a)` are collinear
B. Two collinear vectors are always equal on magnitude
C. Two vectors having same magnitude are collinear
D. Two collinear vectors having the same magnitude are equal

Answer

To determine which of the statements is true regarding vectors, let's analyze each option step by step.

### Step 1: Analyze Option A
**Statement:** A times N minus A times R are collinear.

- **Explanation:** Two vectors are said to be collinear if they lie along the same line or are parallel to each other. In this case, if we consider vector A and its negative counterpart -A, they are indeed parallel and lie on the same line but in opposite directions. Therefore, this statement is true.

### Conclusion for Option A:
**True.**

### Step 2: Analyze Option B
**Statement:** Two collinear vectors are always equal in magnitude.

- **Explanation:** Collinear vectors can have the same or different magnitudes. For example, vector A and vector 2A are collinear, but their magnitudes are different. Hence, this statement is false.

### Conclusion for Option B:
**False.**

### Step 3: Analyze Option C
**Statement:** Two vectors having the same magnitude are also collinear.

- **Explanation:** Two vectors can have the same magnitude but can point in different directions. For example, vector A with a magnitude of 5 and vector B with the same magnitude of 5 but pointing in a different direction are not collinear. Therefore, this statement is false.

### Conclusion for Option C:
**False.**

### Step 4: Analyze Option D
**Statement:** Two collinear vectors having the same magnitude are equal.

- **Explanation:** For two vectors to be equal, they must have both the same magnitude and the same direction. Even if two vectors are collinear and have the same magnitude, if they point in opposite directions (like A and -A), they are not equal. Therefore, this statement is false.

### Conclusion for Option D:
**False.**

### Final Conclusion:
The only true statement among the options is **Option A**.