If |u| = 6,|v| = 11 , and u · v = 1, find |u + v|?

Solution:

Using algebraic identities

|u + v|² = |u|² + 2uv + |v|²

Given:

|u| = 6, |v| = 11, and u · v = 1

Substituting the values in the above equation

|u + v|² = 6² + 2(1) + 11²

By further calculation

|u + v|² = 36 + 2 + 121

So we get

|u + v|² = 159

Taking the square root on the other side

|u + v| = √159

Therefore,

|u + v| = √159

Hence, the required value is √159.

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If |u| = 6,|v| = 11 , and u · v = 1, find |u + v|?

Summary:

If |u| = 6,|v| = 11 , and u · v = 1, |u + v| = √159.