Answer:
Two vectors parallel with vector QP are:
[tex]\vec u = (-\frac{2}{\sqrt{5} },\frac{4}{\sqrt{5} } )[/tex] and [tex]\vec u = (\frac{2}{\sqrt{5} },-\frac{4}{\sqrt{5} } )[/tex].
The parallel vector with same direction is:
[tex]\vec u = (-\frac{2}{\sqrt{5} },\frac{4}{\sqrt{5} } )[/tex]
Step-by-step explanation:
The vector between points P and Q belongs to the following vector family:
[tex]\vec r_{QP} = (2-3,-2+4)[/tex]
[tex]\vec r_{QP} = (-1,2)[/tex]
The norm of this vector is determined by using the definition of norm:
[tex]||\vec r_{QP}|| = \sqrt{5}[/tex]
The unit vector associated to the abovementioned vector family is:
[tex]\vec u_{QP} = (-\frac{1}{\sqrt{5}},\frac{2}{\sqrt{5} } )[/tex]
The parallel vector of length 2 with same direction is obtained by multyplying the previous data by 2:
[tex]\vec s_{QP} = (-\frac{2}{\sqrt{5} },\frac{4}{\sqrt{5} } )[/tex]
Two vectors parallel with vector QP are:
[tex]\vec u = (-\frac{2}{\sqrt{5} },\frac{4}{\sqrt{5} } )[/tex] and [tex]\vec u = (\frac{2}{\sqrt{5} },-\frac{4}{\sqrt{5} } )[/tex].
The parallel vector with same direction is:
[tex]\vec u = (-\frac{2}{\sqrt{5} },\frac{4}{\sqrt{5} } )[/tex]
