Direction Cosines And Direction Ratios Of A Line

To determine the angle at which the normal to the plane is inclined to the y-axis, we first need to identify the normal vector to the plane. The plane equation is of the form . Thus, the normal vector can be derived as .

The angle between the normal vector and the y-axis vector can be found using the dot product formula:

Calculating the dot product:

The magnitude of is:

The magnitude of is:

Substituting these into the cosine formula:

The angle between the y-axis and the normal vector, considering the magnitude, is , but since angles made by normal are conventionally taken as positive, we determine the complementary angle .

Thus, the correct angle is .