The given magnitude of two vectors are 4 and 2.
The sum of magnitude of two vectors is \(2\sqrt{5}\)
Given:
The magnitude of two vectors are 4 and 2.
The direction of two vectors are 45° and 135°.
According to vector addition,
the vector that i drew in red is their sum.
The angle between both the vectors = \(135\)° - \(45\)° = \(90\)°
So, two vectors are perpendicular
Sum = \(\sqrt{4^{2}+2^{2} }\)
\(=\sqrt{16+4} \\=\sqrt{20} \\=2\sqrt{5}\)
Therefore, the sum of magnitude of two vectors is \(2\sqrt{5}\)
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