3 Dimensional Coordinate Geometry

To determine the perpendicularity condition and find the angle between and , we analyze the given direction ratios. Step 1: Find such that The direction ratios of are: The direction ratios of are: Since and are perpendicular, their dot product must be zero: Solving for :
Step 2: Compute the angle between and The direction ratios of are: The angle between two lines is given by the dot product formula: Substituting , we obtain: Since , taking the inverse gives: Alternatively, rewriting in terms of secant: Thus, the correct answer is: Final Answer: .