Direction of |a+b| is south east and that of |a-b| is north east.
Given
a = 3i - 2j
b = -i - 4j
To find,
a+b =?
a-b =?
|a+b| = |(3i - 2j - i - 4j)|
= |2i - 6j|
= [tex]\sqrt{2^{2} + (-6^{2}) }[/tex]
= [tex]\sqrt{4+36}[/tex]
= [tex]\sqrt{40}[/tex]
= [tex]2\sqrt{10}[/tex]
|a-b| = |(3i - 2j) - (-i - 4j)|
= |3i -2j + i + 4j|
= |4i + 2j|
= [tex]\sqrt{4^{2} + 2^{2} } \\[/tex]
= [tex]\sqrt{16+ 4}[/tex]
= [tex]\sqrt{20}[/tex]
= [tex]2\sqrt{5}[/tex]
Direction of |a+b| is south east (|2i - 6j|, this shows 2 units to the right and 6 units down)
Direction of |a-b| is north east (|4i + 2j|, this shows 4 units right & 2 units up)
Learn more about vector calculation here:
https://brainly.com/question/27351405
#SPJ4
