Physics with Dikshant

Dikshant SavantApr 15, 2026

How to Find the Direction of a Resultant Force 📐

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How to Find the Direction of a Resultant Force 📐

Dikshant Savant

Learn how to calculate the direction of a resultant force vector using trigonometry. This tutorial breaks down the formula and steps needed to find the angle alpha relative to your primary vector.

How to Find the Direction of a Resultant Force 📐

Dikshant Savant

Learn how to calculate the direction of a resultant force vector using trigonometry. This tutorial breaks down the formula and steps needed to find the angle alpha relative to your primary vector.

Chapters

00:00

Introduction

Addressing a Reddit question about finding the direction of a resultant force.

00:29

Resultant Force Setup

01:12

The Angle Formula

01:32

Example Calculation

02:44

Community Announcement

Transcript

00:00

Hi.

00:01

I saw your question on Reddit and I think it's a fascinating one.

00:05

You've already found the resultant force and you're asking how do I find the direction of the resulting force?

00:13

So it's very simple.

00:14

yeah.

00:15

Let's take a look at this like you're parting.

00:20

My, has gone to sleep.

00:27

So is it working?

00:29

Yeah.

00:29

Okay, so the resultant force angle is simple.

00:33

Let's say this is A and the angle between your two vectors is theta.

00:40

then your resultant is, as you already calculated, A squared plus B squared plus 2 AB cos theta.

00:47

To find the angle of the resultant force.

00:50

Take a look at this.

00:51

So here is A.

00:52

I've just shifted B over here.

00:54

So now this is B.

00:55

It's still theta.

00:57

This is your resultant force.

00:59

Right?

01:01

And the way you calculated that is basically over here.

01:06

So if I take components of B, this is B cos theta, and this is B sin theta.

01:11

Right?

01:12

And the angle alpha of the resultant vector V R makes with A is alpha.

01:19

Okay?

01:20

So if I write tan of alpha, that will be equal to B sine theta upon A plus b cos theta.

01:30

Right?

01:32

So in your case, tan alpha will become D.

01:39

I'm, taking as 15 into sine 30 upon 10 plus 15 cos 30.

01:49

Simple.

01:50

Right.

01:51

Now this may be a complicated thing because you won't have a natural value of alpha, but you can use a calculator for that.

01:58

So this will be 7.5 sin 30s half 10 plus 7.5 root 3.

02:05

So let's say this answer is, 0.54.

02:09

Let's say.

02:10

I'm assuming, I'm not sure.

02:12

So, just go to any calculator that lets you do tan inverse and tan inverse of 0.4.

02:19

So here you can get the alpha.

02:23

Right.

02:25

Is there something else?

02:27

No, yeah, that's, that's all.

02:30

So here is how you can, find the resultant, angle alpha that the, the force vector makes with the A vector.

02:39

Or in this case, that's a 10 Newton one.

02:42

So hopefully that answers your question.

02:44

I'll just like to pitch in that I have a free school community running right now.

02:49

If you go to schoolskoo.com, right, and if you search for AP Physics 5 Club, you will get this community where you can see physics just got fun and join it.

03:04

I'll, be answering free questions all for the first hundred students.

03:09

So I'll see you there.

03:10

Okay, take care and I'll see you soon.

How to Find the Direction of a Resultant Force 📐 — Tella