If `vecP.vecQ=PQ` then angle between `vecP` and `vecQ` is

Options

A. `0^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

To solve the problem, we need to analyze the given equation and relate it to the properties of vectors. Here’s a step-by-step solution:

### Step 1: Understand the Dot Product
The dot product of two vectors \(\vec{P}\) and \(\vec{Q}\) is given by the formula:
\[ \vec{P} \cdot \vec{Q} = |\vec{P}| |\vec{Q}| \cos(\theta) \]
where \(\theta\) is the angle between the two vectors.

### Step 2: Set Up the Given Equation
According to the problem, we have:
\[ \vec{P} \cdot \vec{Q} = PQ \]
Here, \(PQ\) is interpreted as the product of the magnitudes of \(\vec{P}\) and \(\vec{Q}\).

### Step 3: Substitute the Dot Product Formula
From the dot product formula, we can substitute:
\[ |\vec{P}| |\vec{Q}| \cos(\theta) = |\vec{P}| |\vec{Q}| \]

### Step 4: Simplify the Equation
Now, we can divide both sides of the equation by \(|\vec{P}| |\vec{Q}|\) (assuming neither \(\vec{P}\) nor \(\vec{Q}\) is the zero vector):
\[ \cos(\theta) = 1 \]

### Step 5: Solve for the Angle
The cosine of an angle is equal to 1 when the angle is:
\[ \theta = 0^\circ \]

### Conclusion
Thus, the angle between the vectors \(\vec{P}\) and \(\vec{Q}\) is \(0^\circ\).

### Final Answer
The angle between \(\vec{P}\) and \(\vec{Q}\) is \(0^\circ\).

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