If `(a,b,c)` and `(a^('),b^('),c^(') )` are the direction ratios of two perpendicular lines, then

Options

A. `a//a'=b//b^(')=c//c^(')`
B. aa' +bb' +cc' =0
C. aa'+ bb' + cc' = 1
D. None

Answer

To solve the problem, we need to establish the relationship between the direction ratios of two perpendicular lines in three-dimensional space. Let's denote the direction ratios of the first line as \( (a, b, c) \) and the direction ratios of the second line as \( (a', b', c') \).

### Step-by-step Solution:

1. **Understanding Direction Ratios**:
Direction ratios of a line in three-dimensional space are proportional to the direction cosines of the line. If two lines are represented by their direction ratios, we can treat these ratios as vectors.

2. **Condition for Perpendicularity**:
For two vectors \( \vec{A} = (a, b, c) \) and \( \vec{B} = (a', b', c') \) to be perpendicular, their scalar product (dot product) must be equal to zero. The scalar product is calculated as:
\[ \vec{A} \cdot \vec{B} = a \cdot a' + b \cdot b' + c \cdot c' = 0 \]

3. **Setting Up the Equation**:
From the condition for perpendicularity, we can write:
\[ aa' + bb' + cc' = 0 \]

4. **Conclusion**:
This equation \( aa' + bb' + cc' = 0 \) is the required condition that must be satisfied by the direction ratios of two perpendicular lines.

### Final Statement:
Thus, if \( (a, b, c) \) and \( (a', b', c') \) are the direction ratios of two perpendicular lines, then:
\[ aa' + bb' + cc' = 0 \]