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(a) Let R? be the Euclidean 7-space with cartesian coordinates (11, Y,.I3. Y3. 2) and : M R' defined as (u, v, w, z)

(a) Let R? be the Euclidean 7-space with cartesian coordinates (11, Y,.I3. Y3. 2) and : M R' defined as (u, v, w, z) = (v, u, u cos w, v3vcos w, u sin w, v3 vsin w, z), u, v# 0; embeds M into R'. -(i) Find the basis of the tangent space of M. (ii) Compute the metric on M induced by p.

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