Answer :
Answer:
a)The component form is
[tex]\vec {QP}=\binom{ - 1}{ - 8} [/tex]
b)The magnitude is √65
c) <2,14>
Step-by-step explanation:
Recall that:
[tex]\vec {QP}=\vec {OP}-\vec{OQ}[/tex]
We substitute the position vectors to get:
[tex]\vec {QP}=\binom{ - 8}{7} - \binom { - 7}{15} [/tex]
We subtract the corresponding components to obtain:
[tex]\vec {QP}=\binom{ - 8 - - 7}{7 - 15} [/tex]
This gives:
[tex]\vec {QP}=\binom{ - 8 + 7}{7 - 15} [/tex]
This simplifies to:
[tex]\vec {QP}=\binom{ - 1}{ - 8} [/tex]
The magnitude of a vector in the component form:
[tex] \binom{x}{y}[/tex]
is
[tex] \sqrt{ {x}^{2} + {y}^{2} } [/tex]
This means:
[tex] |\vec {QP}|= \sqrt{ {( - 1)}^{2} + {( - 8)}^{2} } [/tex]
This simplifies to:
[tex] |\vec {QP}| = \sqrt{ 1 + 64 } [/tex]
[tex] |\vec {QP}| = \sqrt{ 65 } [/tex]
c) We have the vectors u = <4, 8>, v = <-2, 6>.
We want to find:
u+v
This implies that:
u+v=<4,8>+<-2,6>
We add the corresponding components to get;
u+v=<4+-2,8+6>
This simplifies to:
u+v=<2,14>