Answer:
[tex] Magnitude =\sqrt{59} \\\\
Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}}
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Step-by-step explanation:
A=2i+3j+4k
B=i-2j+3k
Sum of the vectors:
A + B = 2i+3j+4k + i-2j+3k = 3i + j + 7k
[tex] Magnitude =\sqrt{3^2 + 1^2+ 7^2} \\\\
Magnitude =\sqrt{9+1+49} \\\\
Magnitude =\sqrt{59} [/tex]
Direction of the sum of the vectors:
[tex] \widehat{A + B} =\frac{\overrightarrow{A + B}}{Magnitude\: of \:\overrightarrow{A + B}} \\\\
\widehat{A + B} =\frac{3i + j + 7k}{\sqrt {59}} \\\\
\widehat{A + B} =\frac{3}{\sqrt {59}} i +\frac{1}{\sqrt {59}} j+\frac{7}{\sqrt {59}} k\\\\
Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}} \\\\
[/tex]
