Question

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 

Answer 1

The magnitude of $\bold c = 2 \bold a + 3 \bold b$ is:

$|\bold c| = \sqrt{<2 \bold a+ 3 \bold b, 2 \bold a + 3 \bold b>} = \sqrt{4 |\bold a|^2 + 12<\bold a, \bold b> + 9 |\bold b|^2} = \sqrt{4 \cdot 16 + 12 \cdot 4 \cdot 6 \cdot \cos 60 + 9 \cdot 36} = \sqrt{532} = 2 \sqrt{133}$