any idea how to answer these questions this is original post

any idea how to answer these questions?

this is original post and the professor had those follow up questions

Thank you

Sunday Great applications of the dot product. Knowing that And why is V·V 1.112 Reply

v = 7i + j

w = i + 7j

v.w = a1 a2 + b1b2

a1 = 7 ( first component of v vector ) and a2 = 1 ( first component of w vector )

b1 = 1 ( 2nd component of v vector ) and b2 = 7 ( 2nd component of w vector )

a1 a2 + b1 b2 = 7*1 + 1*7

= 14

hence, v.w = 14

b) since we have to find dot product of v .v

so we will use components of v now

v.v = (7*7 ) + (1*1)

49 + 1

= 50