Question

determine whether the vectors in each pair are normal
u=(2,2) and v=(4,-1)
p=(3,-2) and q=(4,6)
a=(7,-1) b=(1,7)

Answer 1

Hint : dot product

Answer 2

We only had one lesson over vectors so I don't really understand them at all...

Answer 3

@ganeshie8

Answer 4

Okay, what do you know about dot product ?

Answer 5

Pretty much nothing...

Answer 6

\(\color{red}{\vec{a} = (a_1, a_2)}\)
\(\vec{b} = (b_1, b_2)\)

\[\color{Red}{\vec{a}} \cdot \vec{b} = \color{red}{a_1}b_1 + \color{red}{a_2}b_2 \]

Answer 7

dot product is one way of defining multiplication of two vectors

Answer 8

to find the dot product of two vectors you just `multiply the corresponding components` and `add` them

Answer 9

Okay how do I know if the vectors are normal?

Answer 10

if the dot product of two vectors is 0, then the vectors are normal

Answer 11

simply find the dot product of given vectors and see if you get 0

Answer 12

so they aren't normal? I got -16

Answer 13

for what vectors ?

Answer 14

Lets see if these vectors are normal :
\(\vec{u}=(2,2)\)
\(\vec{v}=(4,-1)\)

\(\vec{u}\cdot \vec{v} = 2(4) + 2(-1) = 8-2 = 6 \ne 0\)

so the vectors \(\vec{u}\) and \(\vec{v}\) are not normal