For the spherical surface x² + y² + z² = 1, the unit outward normal vector at the point (1/√2, 1/√2, 0) is given by

Question

Accepted Answer

1/√2 î + 1/√2 ĵ. The unit outward normal vector at a point on a sphere is simply the normalized position vector from the origin to that point. At (1/√2, 1/√2, 0), the vector is (1/√2, 1/√2, 0), which, when normalized, remains the same since its magnitude is already 1 in the x-y plane.

For the spherical surface x² + y² + z² = 1, the unit outward normal vector at the point (1/√2, 1/√2, 0) is given by

Solution

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