Q1P Draw diagrams and prove (4.1).... [FREE SOLUTION]

Chapter 3: Q1P (page 99)

Draw diagrams and prove (4.1).

Short Answer

Expert verified

The diagram is verified using (4.1) theorem.

Step by step solution

Formula for the magnitude of the components of the vector:

If $A_{x}, A_{y},$ and $A_{z}$ are the magnitudes of components of vector $\overset{鈫�}{A}$ along the coordinate axis, then $\overset{鈫�}{A} = A_{x} \hat{i} + A_{y} \hat{j} + A_{z} \hat{k}$ , where $\hat{i}, \hat{j}, \hat{k}$ respectively are the unit vectors along $x, y$ and zaxis.

The diagram of vector A→ in two dimensions:

Using Pythagoras theorem, the length of A , named $A = | A |$ is given by,

$A^{2} = A_{x}^{2} + A_{y}^{2} A = \sqrt{A_{x}^{2} + A_{y}^{2}}$

Where the dotted lines represent the components of the vector $A_{x}$ and $A_{y}$

The diagram of vector A→ in three dimensions:

Using Pythagoras theorem in $3 D$ , the length of A , named $A = | A |$ is given by,

$A^{2} = A_{x}^{2} + A_{y}^{2} + A_{z}^{2} A = \sqrt{A_{x}^{2} + A_{y}^{2} + A_{z}^{2}}$

Where the dotted lines represent the components of the vector $A_{x}, A_{y}$ and $A_{z}$ .

Hence, the condition is proved.

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Draw diagrams and prove (4.1).

Short Answer

Step by step solution

Formula for the magnitude of the components of the vector:

The diagram of vector A→ in two dimensions:

The diagram of vector A→ in three dimensions:

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