Question

Vector A has magnitude 4 units, vector B has magnitude 6 units. The angle between A and B is 60 degrees. Calculate the magnitude of 2A + 3B.

Answer 1

Explanations & Calculations

• What is asked is the vector addition of 2 vectors and the included angle is given.
• In such a case, using the equation $\small R^2=P^2+Q^2+2PQ\cos\theta$, the magnitude of their resultant (R) can be calculated.

• Now the two forces are $\small \vec{P}=2\vec{A}$ and $\small \vec{Q}=3\vec{B}$
• Then the corresponding magnitudes are

$\qquad\small |\vec{P}|=P=|2\vec{A}|=2|\vec{A}|=2\times4units=8\,units$

$\qquad\small |\vec{Q}|=Q=|3\vec{Q}|=3|\vec{Q}|=3\times6\,units=18\,units.$

• Then plugging these data in the above equation,

$\qquad\qquad \begin{aligned} \small R^2&=\small8^2+18^2+2(8)(18)\cos60\\ &=\small 532\,units^2 \\ \small R &=\small \bold{23.065N} \end{aligned}$