egbeach
  • egbeach
Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <6, -2>, v = <8, 24>
Mathematics
jamiebookeater
  • jamiebookeater
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UsukiDoll
  • UsukiDoll
the vectors are orthogonal if the result is 0 after using the dot product. \[u \cdot v = \]
anonymous
  • anonymous
If vectors are parallel, then there exists a scalar \(c\) such that\[ \mathbf u = c \mathbf v \]
UsukiDoll
  • UsukiDoll
\[u \cdot v = \] for dot product but if it's neither than the dot product can't be 0 and a scalar c doesn't exist.

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egbeach
  • egbeach
do i just plug in the numbers to solve?
UsukiDoll
  • UsukiDoll
you could.. since we have \[u=, v=\] and we can use dot product \[u \cdot v = \]
UsukiDoll
  • 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 \[u \cdot v = u_1v_1+u_2v_2\]
UsukiDoll
  • UsukiDoll
\[u \cdot v = (6)(8)+(-2)(24) \]
UsukiDoll
  • UsukiDoll
so what is 6 x 8 and what is -2 x 24 ?
egbeach
  • egbeach
6x8=48 -2x24= -48
UsukiDoll
  • UsukiDoll
mhm \[u \cdot v = 48-48 \] so now what's 48-48?
egbeach
  • egbeach
0. so is it neither?
UsukiDoll
  • UsukiDoll
no.. since our dot product is 0, our vectors are _______________
egbeach
  • egbeach
orthogonal since it equal 0
UsukiDoll
  • UsukiDoll
yes :)

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