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Consider the two vectors a 3i-2j & b = -i-4j calculate the direction of a+b and a-b?

Sagot :

Tutorconsortium330

Direction of |a+b| is south east and that of |a-b| is north east.

Calculation:

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

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