Let u v be two vectors in the inner product space R15 with r

Let u, v be two vectors in the inner product space R^15 with respect to the usual dot product. Suppose u · v = 0, ||u|| = 7, ||v|| = 2. Then what is the value of ||2u v||?

A. 4

B. 2 2

C. 4 2

D. 4 3

E. None of the above

|| 2u -v||

= sqrt ( (2u-v) . (2u-v) )

= sqrt( 2u.2u - 2u.v -2u.v + v.v)

= sqrt(4 || u ||^2 + || v||^2 )

= sqrt ( 4 *7 + 4)

= sqrt(32)

= 4 * sqrt(2)

so the correct choice is C

Let u, v be two vectors in the inner product space R^15 with respect to the usual dot product. Suppose u · v = 0, ||u|| = 7, ||v|| = 2. Then what is the value o

Let u v be two vectors in the inner product space R15 with r

Solution

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