Answer:
1a) a) [tex]\overrightarrow {\alpha} = (-10,-16)[/tex], 1b) [tex]\| \overrightarrow {\alpha} \| = 2\sqrt{89}[/tex], 2a) [tex]\overrightarrow {\alpha} = (-14,-21)[/tex], 2b) [tex]\| \overrightarrow {\alpha} \| = 7\sqrt{13}[/tex], 3a) [tex]\overrightarrow {\alpha} = (-18,-26)[/tex], 3b) [tex]\| \overrightarrow {\alpha} \| = 10\sqrt{10}[/tex]
Step-by-step explanation:
1a) The vectors [tex]\overrightarrow {PQ}[/tex] and [tex]\overrightarrow {RS}[/tex] are determined:
[tex]\overrightarrow {PQ} = (7-5,3-4)[/tex]
[tex]\overrightarrow {PQ} = (2, -1)[/tex]
[tex]\overrightarrow {RS} = (4-8,1-6)[/tex]
[tex]\overrightarrow {RS} = (-4, -5)[/tex]
The component form of the resultant vector is:
[tex]\overrightarrow {\alpha} = (2 -12, -1-15)[/tex]
[tex]\overrightarrow {\alpha} = (-10,-16)[/tex]
1b) The magnitude of the resultant vector is:
[tex]\| \overrightarrow {\alpha} \| = \sqrt{(-10)^{2}+(-16)^{2}}[/tex]
[tex]\| \overrightarrow {\alpha} \| = 2\sqrt{89}[/tex]
2a) The vectors [tex]\overrightarrow {PQ}[/tex] and [tex]\overrightarrow {RS}[/tex] are determined:
[tex]\overrightarrow {PQ} = (7-5,3-4)[/tex]
[tex]\overrightarrow {PQ} = (2, -1)[/tex]
[tex]\overrightarrow {RS} = (4-8,1-6)[/tex]
[tex]\overrightarrow {RS} = (-4, -5)[/tex]
The component form of the resultant vector is:
[tex]\overrightarrow {\alpha} = (2 -16, -1-20)[/tex]
[tex]\overrightarrow {\alpha} = (-14,-21)[/tex]
2b) The magnitude of the resultant vector is:
[tex]\| \overrightarrow {\alpha} \| = \sqrt{(-14)^{2}+(-21)^{2}}[/tex]
[tex]\| \overrightarrow {\alpha} \| = 7\sqrt{13}[/tex]
3a) The vectors [tex]\overrightarrow {PQ}[/tex] and [tex]\overrightarrow {RS}[/tex] are determined:
[tex]\overrightarrow {PQ} = (7-5,3-4)[/tex]
[tex]\overrightarrow {PQ} = (2, -1)[/tex]
[tex]\overrightarrow {RS} = (4-8,1-6)[/tex]
[tex]\overrightarrow {RS} = (-4, -5)[/tex]
The component form of the resultant vector is:
[tex]\overrightarrow {\alpha} = (2 -20, -1-25)[/tex]
[tex]\overrightarrow {\alpha} = (-18,-26)[/tex]
3b) The magnitude of the resultant vector is:
[tex]\| \overrightarrow {\alpha} \| = \sqrt{(-18)^{2}+(-26)^{2}}[/tex]
[tex]\| \overrightarrow {\alpha} \| = 10\sqrt{10}[/tex]
