If `a.b = a.c` and `veca xx vecb` =`veca xx vecc`, then

Options

A. a is perpendicular to `b-c`
B. a is parallel to `b-c`
C. either `a = 0 or b = c`,
D. none of these

Answer

To solve the problem given the equations \( \vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} \) and \( \vec{a} \times \vec{b} = \vec{a} \times \vec{c} \), we will analyze each equation step-by-step.

### Step 1: Analyze the first equation
We start with the first equation:
\[ \vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} \]
Rearranging this gives:
\[ \vec{a} \cdot \vec{b} - \vec{a} \cdot \vec{c} = 0 \]
Factoring out \( \vec{a} \):
\[ \vec{a} \cdot (\vec{b} - \vec{c}) = 0 \]