Vector 𝑨⃗ has magnitude 4 units, vector 𝑩⃗⃗ has magnitude 6 units. The angle between 𝑨⃗ and 𝑩⃗⃗ is 60. Calculate the magnitude of 2𝑨⃗ + 3𝑩⃗⃗
The magnitude of "\\bold c = 2 \\bold a + 3 \\bold b" is:
"|\\bold c| = \\sqrt{<2 \\bold a+ 3 \\bold b, 2 \\bold a + 3 \\bold b>} = \\sqrt{4 |\\bold a|^2 + 12<\\bold a, \\bold b> + 9 |\\bold b|^2} = \\sqrt{4 \\cdot 16 + 12 \\cdot 4 \\cdot 6 \\cdot \\cos 60 + 9 \\cdot 36} = \\sqrt{532} = 2 \\sqrt{133}"
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