Q26DQ

Question

If $\vec{A}$ = 0 for a vector in the xy-plane, does it follow that A_x = -A_y? What can you say about A_x and A_y?

Step-by-Step Solution

Verified

Answer

Given- $\vec{A}$ and $\vec{B}$ are vector The sum of number of vectors that for the sum of two vectors is geometrically represented by the diagonal of parallelogram whose side represent the two vectors being added.

$\vec{A} = 0$ ,for a vector in the xy plane.

1Step1 - To Prove

$A_{x}$ = - $A_{y}$

2Step 2 (Explaination and proof of Ax = -Ay)=0

If $\vec{A}$ =0

Such that $\vec{A}$ is in xy plane.

i.e. $\vec{A}$ = ${\vec{A}}_{x} \hat{i} + {\vec{A}}_{y j}$

3Step 3 ( Explaination )

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

$\vec{A}$ = 0 = $\sqrt{A_{x}^{2} + A_{y}^{2}}$

$A_{x}^{2}$ + $A_{y}^{2}$ =0

The only case possible is

$A_{x}$ = $A_{y}$ =0

4Step 4 (Conclusion)

It is proved

$A_{x}$ is not equal to - $A_{y}$

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