Question

precalc givin medals
1. Let u = <-4, 1>, v = <-1, 6>. Find -2u + 4v.
<4, 22>
<4, 7>
<12, -26>
<10, -14>

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

u = <3, 0>, v = <0, -6>

Orthogonal
Neither
Parallel

Answer 1

u is a vector
the -2 in front of the vector u is a scale factor
it is just a number you multiply to each component of u

Answer 2

from number 2 have you considered finding the dot product?

Answer 3

and the magnitudes of the vectors as well

Answer 4

\[\cos(\theta)=\frac{a \cdot b}{|a| \cdot |b|} \\ \theta=\arccos( \frac{ a \cdot b}{|a| \cdot |b|}) \\ \text{ if } \theta=90^o \text{ then } a \text{ and } b \text{ are orthogonal } \\ \text{ but to find out if they are orthogonal you only need to see if } a \cdot b=0 \\ \text{ this is much shorter than actually finding the angle between the two vectors }\]
\[\text{ if } \theta=0^o \text{ or } \theta=180^o \text{ then you have that } a \text{ and } b \\ \text{ are parallel } \\ \text{ but you don't really need to find } \theta \\ \text{ you could just see if } a \cdot b=|a| \cdot |b| \text{ or if } a \cdot b =-|a| \cdot |b|\]

Answer 5

@freckles orthogonal?

Answer 6

u and v are definately orth as one is completely in x and the onther is in y