Which of the following statements is false regarding the vectors?

Options

A. The magnitude of a vector is always a scalar
B. Each component of a vector is always a scalar.
C. Two vectors having different magnitudes cannot have their resultant zero
D. Vectors obey triangle law of addition

Answer

To determine which of the statements regarding vectors is false, we will analyze each statement one by one.

### Step 1: Analyze the first statement
The first statement claims that "the magnitude of a vector is always a scalar quantity."

- **Explanation**: This statement is true. The magnitude of a vector is indeed a scalar quantity because it only has a size and no direction.

### Step 2: Analyze the second statement
The second statement claims that "each component of a vector is always a scalar quantity."

- **Explanation**: This statement is false. Each component of a vector is itself a vector quantity. For example, if we have a vector \( \mathbf{r} \) expressed in terms of its components along the x and y axes, \( \mathbf{r} = r_x \hat{i} + r_y \hat{j} \), both \( r_x \) and \( r_y \) are vector components, not scalars.

### Step 3: Analyze the third statement
The third statement claims that "two vectors having different magnitudes cannot have their resultant zero."

- **Explanation**: This statement is true. For two vectors to have a resultant of zero, they must be equal in magnitude and opposite in direction. If their magnitudes are different, they cannot cancel each other out, and thus their resultant cannot be zero.

### Step 4: Analyze the fourth statement
The fourth statement claims that "vectors obey the triangle law of addition."

- **Explanation**: This statement is true. The triangle law of addition states that if two vectors are represented as two sides of a triangle taken in order, then their resultant is represented by the third side of the triangle taken in the opposite order.

### Conclusion
Based on the analysis:
- The first statement is true.
- The second statement is false (this is the answer we are looking for).
- The third statement is true.
- The fourth statement is true.

Thus, the false statement regarding vectors is the second one: "each component of a vector is always a scalar quantity."

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