# What is Resultant Vector? [closed]

I tried to solve the given question in the following way. Where I am going wrong?

Q. Let $$\vec A$$ and $$\vec B$$ be the two vectors of magnitude $$10$$ unit each. If they are inclined to the $$x$$-axis at angles $$30^\circ$$ and $$60^\circ$$ respectively, find the resultant.

I tried to solve the question in this way $$\rightarrow$$
Let, the angle between A and B = $$\theta$$
$$\therefore\ \theta=60^\circ-30^\circ=30^\circ$$
$$\therefore\ |\vec R| = \sqrt{A^2+B^2+2AB \cos\theta}$$
= $$\sqrt{10^2+10^2+2\cdot10\cdot10\cos30^\circ}$$
= $$\sqrt{100+100+200\,\sqrt3/2}$$
= $$\sqrt{100+100+100\,\sqrt3}$$
= $$\sqrt{200+100\,\sqrt3}$$
= $$\sqrt{100\,(2+\sqrt3)}$$
= $$10\,\sqrt{2+\sqrt3}$$

Now, I don't know how to solve it further. The answer is $$20 \cos 15^\circ$$. Please help me to simplify it further.

$$\cos 15^\circ = \frac{1+\sqrt3}{2\sqrt2}.$$

• Welcome to Physics Stack Exchange! Please take a minute to read our guidelines for homework and exercise questions as well as check-my-work questions. We intend our questions to be potentially useful to a broader set of users than just the one asking, and we prefer conceptual questions over those just asking for a specific computation. May 3, 2021 at 10:39
• The question phrasing must also state that the two vectors should be added together or have some other arithmetic operation done. Otherwise it makes no sense to ask for the resultant vector. May 3, 2021 at 10:48
• To give a hint, I would write out the two vectors with their coordinates. And then add together those vectors, coordinate by coordinate. And then you have the resultant vector. If you need the magnitude, then you can extract/calculate it from this resultant vector - if you need the angle, then same. May 3, 2021 at 10:51