Question

If (u) = 11, (v) = 23, and (u-v) = 30.

Find (u+v)

Answer 1

The Law of Cosines

$$30^2=11^2+23^2-2(11)(23)\cos \theta$$

$$\cos \theta=-\dfrac{125}{253}$$

$$|\vec{u}+\vec{v}|^2=11^2+23^2+2(11)(23)\cos \theta$$

$$|\vec{u}+\vec{v}|=\sqrt{11^2+23^2-2(11)(23)(\dfrac{125}{253})}$$

$$|\vec{u}+\vec{v}|=20$$