Suppose that u and v are vectors and that ||u||=4 and ||v||=10. Which of the fol

Question

Suppose that u and v are vectors and that ||u||=4 and ||v||=10.
Which of the following could be the value of u (dot) v ? Select all that apply.

A. 43

B. 35

C. -80

D. -37

E. -20

F. -40

G. 80

H. 0

I. -45

J. 10

K. 20

L. 4

M. 40

Which of the following could be the value of |u+v| ? Select all that apply.

A. 8

B. 24

C. 6

D. -14

E. 4

F. 18

G. 1

H. 10

I. 14

For the 1st part I chose all values whose absolute value is less than or equal to 40, and for the second I chose all values whose absolute value is less than or equal to 14, which wasn't right

Explanation / Answer

|<u,v>| <= |u||v|

Therefore u dot v must be bounded by 40 magnitude wise

B, D, E, F, H, J, K L, M

|u+v| <= |u|+|v|

This must be bounded by 14 but must also be positive because |u+v| >= 0

A,C,E,G H,I

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