Question

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <7, -4>, v = <-28, 16>

Answer 1

take the dot product, if it equal zero the vectors are orthogonal

Answer 2

How do you take the dot product?

Answer 3

\[\mathbf a=\langle a_1,a_2\rangle\\\mathbf b=\langle b_1,b_2\rangle\]\[\mathbf a\cdot \mathbf b=\langle a_1,a_2\rangle\cdot\langle b_1,b_2\rangle=a_1b_1+a_2b_2\]

Answer 4

\[\mathbf c=\langle c_1,c_2\rangle\\\mathbf d=\langle d_1,d_2\rangle\]
if the vectors are parallel one will be a scaler multiple of the other
\[\mathbf c=\langle c_1,c_2\rangle=\langle \alpha d_1,\alpha d_2\rangle=\alpha \langle d_1,d_2\rangle=\alpha\mathbf d\]

Answer 5

Thank you so much for your help !

Answer 6

note: the scalar can be negative