## anonymous one year ago Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <6, -2>, v = <8, 24>

1. UsukiDoll

the vectors are orthogonal if the result is 0 after using the dot product. $u \cdot v =<u_1v_1,u_2v_2,...u_nv_n>$

2. anonymous

If vectors are parallel, then there exists a scalar $$c$$ such that$\mathbf u = c \mathbf v$

3. UsukiDoll

$u \cdot v = <u_1v_1+u_2v_2+...u_nv_n>$ for dot product but if it's neither than the dot product can't be 0 and a scalar c doesn't exist.

4. anonymous

do i just plug in the numbers to solve?

5. UsukiDoll

you could.. since we have $u=<u_1,u_2>, v=<v_1,v_2>$ and we can use dot product $u \cdot v = <u_1v_1+u_2v_2+...u_nv_n>$

6. UsukiDoll

u= <6,-2> and v = <8,24> $u_1=6,u_2=-2,v_1=8,v_2=24$ now we plug those values into the dot product formula $u \cdot v = u_1v_1+u_2v_2$

7. UsukiDoll

$u \cdot v = (6)(8)+(-2)(24)$

8. UsukiDoll

so what is 6 x 8 and what is -2 x 24 ?

9. anonymous

6x8=48 -2x24= -48

10. UsukiDoll

mhm $u \cdot v = 48-48$ so now what's 48-48?

11. anonymous

0. so is it neither?

12. UsukiDoll

no.. since our dot product is 0, our vectors are _______________

13. anonymous

orthogonal since it equal 0

14. UsukiDoll

yes :)