If `vec(A)` is a vector of magnitudes `5 units` due east. What is the magnitude and direction of a vector `-5vec(A)`?

Options

A. 5 units due east
B. 25 units due west
C. 5 units due west
D. 25 units due east

Explanation

To solve the problem, let's break it down step by step.

### Step 1: Understand the given vector
We have a vector \( \vec{A} \) with a magnitude of \( 5 \) units directed due east. In vector notation, we can represent this as:
\[ \vec{A} = 5 \hat{i} \]
where \( \hat{i} \) is the unit vector in the east direction.

### Step 2: Calculate the vector \(-5\vec{A}\)
To find the vector \(-5\vec{A}\), we multiply the vector \( \vec{A} \) by \(-5\):
\[ -5\vec{A} = -5 \times (5 \hat{i}) = -25 \hat{i} \]

### Step 3: Determine the magnitude of \(-5\vec{A}\)
The magnitude of the vector \(-25 \hat{i}\) is simply the absolute value of the coefficient:
\[ \text{Magnitude} = |-25| = 25 \text{ units} \]

### Step 4: Determine the direction of \(-5\vec{A}\)
The direction of the vector \(-25 \hat{i}\) is opposite to that of \(5 \hat{i}\). Since \(5 \hat{i}\) points east, \(-25 \hat{i}\) points west.

### Final Answer
Thus, the magnitude of the vector \(-5\vec{A}\) is \(25\) units, and its direction is west.

### Summary
- Magnitude: \(25\) units
- Direction: West

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