For the vectors A⃗ and B⃗ in Fig 134 , use the method of components to find the magnitude and di

step 1 So we are given. Well, there it is. Eighteen years downwards on Victor Bea. It is has magnitude

For the vectors A⃗ and B⃗ in Fig 134 , use the method of...

For the vectors $\vec{A}$ and $\vec{B}$ in Fig 134 , use the method of components to find the magnitude and direction of (a) the vector sum $\vec{A}+\vec{B}$ (b) the vector sum $\vec{B}+\vec{A}$ (c) the vector difference $\overrightarrow{\boldsymbol{A}}-\overrightarrow{\boldsymbol{B}} ;$ (d) the vector difference $\overrightarrow{\boldsymbol{B}}-\overrightarrow{\boldsymbol{A}}$

Key Concepts

Direction Calculation

Determining the direction of a vector involves calculating the angle it makes with a reference axis, typically using trigonometric functions. The inverse tangent function (arctan) is used to find the angle from the ratio of the y-component to the x-component, while adjustments are made depending on the signs of the components to establish the correct quadrant.

Magnitude Calculation

The magnitude of a vector represents its length or size and is determined by applying the Pythagorean theorem to its components. When a vector is expressed with x and y components, its magnitude is calculated as the square root of the sum of the squares of the components.

Method of Components

This concept involves breaking down a vector into its orthogonal components, typically along the x and y axes. It simplifies problems in vector arithmetic by allowing separate manipulation of the horizontal and vertical parts, making operations such as addition and subtraction straightforward.

Vector Addition and Subtraction

Vector addition is the process of combining two or more vectors by adding their corresponding components, resulting in a new vector known as the resultant. Vector subtraction involves adding the negative of a vector, highlighting that these operations depend on the component values. Both operations are central to solving problems involving multiple vector quantities.

Transcript

00:02 So we are given.

00:04 Well, there it is.

00:07 Eighteen years downwards on victor bea.

00:12 It is has magnitude off fifteen units.

00:15 Aunt has that makes an army officer davis, with my access as you should accept his horizontal honor y axis is what no, we can find out the confidence off sector b.

00:30 This conference, which is b x, the x confident off better be would be fifteen signed thirty, which would be seven point five minutes.

00:42 That's the vertical confident off b, which is b y would be in cost thirty, which would be thirteen units.

00:52 Hence.

00:53 We can write a because it is completely in the white direction on this downwards and has eighteen.

00:59 Its amplitude is minus a j and b will be b x.

01:07 I can be way by jacob, which would be seven point five.

01:14 Let's thirteen.

01:14 Jake, no, we need to find out a lesbian now.

01:22 Director, eh? it's like this on when we add victor beat to it a result and victor should look something like this.

01:31 But we can simply our director's using our yoon effect er's.

01:35 It would be minus a chacha.

01:38 Let's be would be seven point five.

01:43 That's thirty in jamaica.

01:45 Now, when you add this to conference, we can see that a plus b is seven point five.

01:54 Let's file jaeger, which, if it means this vector would have a ex confident off seven point five on the white conference off five.

02:07 Now to find people, you know that our victor bea is like this and then later a is like this and hence r b percent.

02:20 There will be something like this.

02:23 Now we can simply use the same matter here.

02:25 Letter b is seven point five.

02:30 I can't let's thirteen check less...

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