Gradient of the function:

.

The gradient of the vector is normal to the level surfaces.

(a)

The equations are , and the point is .

Rewrite the equation as .

Consider .

Find gradient of the function .

.

Substitute the point in above equation.

Rewrite the equation as .

Consider .

Find gradient of the function .

.

Substitute the point in above equation.

The cross product of these two gradients is a vector that is tangent to

both surfaces at the point .

Symmetric equations:

(b)

Dot product is .

Two vectors are orthogonal if and only if the dot product is zero.

Since , the vectors are not orthogonal.

(a) Symmetric equations are .

(b) The cosine angle is , the surfaces are not orthogonal.