can you please answer this question part a and b

fill in blank

Let v ,w R^n with ||v ||=5 and ||w ||=6. Prove that ||v +w ||=11 if and only if 5w =6v . There are two parts to the proof. Suppose 5w =6v Then w =__________ v and v +w =v +___________ v =___________ v . Thus ||v +w ||=||__________v ||=___________ ||v ||= __________

Suppose ||v +w ||=11. By the triangular inequality, ||v +w ||||v ||+||w ||=__________________

It follows that v and w are in the same direction, i.e._________________ Where k=_________________ . Hence 5w =6v .

Q.E.D.

b)

options for m/c

A. ||u v ||||u +v ||

B. u v =0

C. (u u +v v )2(u v)

D. ||u ||^2+||v ||||u ||||v ||||u ||+||v ||^2

E. (u1,u2,u3)(v1,v2,v3)=0

F. (u v )(u v )

Let u and v be orthogonal vectors in Rn, prove that ||u v ||^2=||u ||^2+||v ||^2.

Proof:

Since u and v are orthogonal then_____________ from which it follows that,

||u v ||^2= _________ = ____________=||u ||^2+||v ||^2

(1 point) 4 Find the projection of v 7 onto the line L with vector equation i wala t where d 4 -6 5 proj = Note: You can earn partial credit on this problem. (1 point) 4 Find the projection of v 7 onto the line L with vector equation i wala t where d 4 -6 5 proj = Note: You can earn partial credit on this