Coplanarity Of Two Lines

Step 1: Concept:
• Two lines are coplanar if the scalar triple product is zero:

Step 2: Identify Vectors:
• Point on Line 1: , direction:
• Point on Line 2: , direction:
• Vector joining points:

Step 3: Apply Determinant Condition:
• Scalar triple product:
• Expanding:
• Simplify:
• Rearranging:

Step 4: Final Answer:
• Factorize:
•

Step 1: Use the given equation.
We are given that . Using the formula for the magnitude of the difference of two vectors: Since and are unit vectors, , so the equation simplifies to:
Step 2: Substitute the given magnitude.
Substitute into the equation: Square both sides:
Step 3: Solve for .
Rearrange the equation: So:
Step 4: Find the angle between and .
The dot product of two vectors is given by: Thus: Therefore, the angle is: Thus, the angle between and is: