The angle between the lines x= y , z =0 and y =0, z =0 is

Step-by-step solution

The angle between two lines can be determined by the angle between their direction vectors. Line x=y , z=0 has direction vector d ₁ = 1, 1, 0 . Line y=0 , z=0 (the x -axis) has direction vector d ₂ = 1, 0, 0 . The cosine of the angle satisfies = | d ₁ d ₂| | d ₁ | | d ₂ | . Compute the dot product: d ₁ d ₂ = 1 1 + 1 0 + 0 0 = 1 . Compute magnitudes: | d ₁ | = 1^2 + 1^2 + 0^2 = 2 , | d ₂ | = 1^2 + 0^2 + 0^2 = 1 . So = 1 2 1 = 1 2 , giving = rccos ( 1 2 ) = 45^ . The angle between the lines is 45^ . The correct choi