Question

Please answer ASAP with explanation.

Vectors $\overrightarrow{\sf{A}}$ and $\overrightarrow{\sf{B}}$ lie in the x - y plane. We can deduce that $\overrightarrow{\sf{A}} = \overrightarrow{\sf{B}}$ if

$\pink{\bf{(A)} \; \; \sf{A^2_x + A^2_y = B^2_x + B^2_y}}$
$\purple{\bf{(B)} \; \; \sf{A_x + A_y = B_x + B_y}}$
$\red{\bf{(C)} \; \; \sf{A_x = B_x \; and \; A_y = B_y}}$
$\green{\bf{(D)} \; \; \sf{\dfrac{A_y}{A_x} = \dfrac{B_y}{B_x}}}$​

Answer 1

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\maltese \; {\underline{\underline{\textbf{\textsf{Stated that :}}}}}$

• The two vectors $\vec{A}$ and $\vec{B}$ lie in the x - y plane

$\maltese \; {\underline{\underline{\textbf{\textsf{To Find :}}}}}$

• Which statement would be true if $\vec{A} = \vec{B }$

$\maltese \; {\underline{\underline{\textbf{\textsf{Given Options :}}}}}$

• $\sf A^2_x + A ^2_y = B^2_x + B^2_y$    
• $\sf A_x + A_y = B_x + B_y$  
• $\sf A_x = B_x \; and \; A_y = B_y$    
• $\sf \dfrac{A_y}{A_x} = \dfrac{B_y}{B_x}$  

$\maltese \; {\underline{\underline{\textbf{\textsf{Required Solution :}}}}}$

We know that when any of the two vectors  are parallel to each other and have the same magnitude then,  The  ratio of the positions of the 1st vector is equal to the ratio of the second vector irrespective to the units $\bf \hat{i}$ and $\bf \hat{j}$ when in the x - y plane

Then if  $\sf A_x = B_x \; and \; A_y = B_y$ satisfies, we can state that the two vectors which lie in the x - y are equal to each other in both magnitude and direction  

• Thereby the 3rd option $\bf(c) \; \sf \sf A_x = B_x \; and \; A_y = B_y$  is correct  

Similarly if the vectors would lie in the x - y - z plane , which means

$\rightarrow \bf \vec{A} = A_x \hat{i} + A_y \hat{J} + A_z \hat{k} = \bf \vec{B} = B_x \hat{i} + B_y \hat{J} + B_z \hat{k}$

then, $\sf A_x = B_x \; and \; A_y = B_y \; and \; A_z = B_z$ would be applicable

$\maltese \; {\underline{\underline{\textbf{\textsf{More To Know :}}}}}$

• The magnitude of a resultant vector is that $\bf |\vec{r}| = \sqrt{x^2 + y^2 + z^2}$
• The dot product of 2 vectors is given by $\bf \vec{A} . \vec{B} = AB \cos (\theta)$
• The magnitude of a vector is a scalar quantity
• the unit vector of it's direction is given by $\bf \hat{a} = \dfrac{\hat{A}}{|\hat{A} |}$  

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

Answer:

Hey bruh ! @LetsHelp123

My iñsta acçount is scarletwitch171 !

Please do inform to Lavanya sis too ! My answer was deleted to your question, my fault anyway.

Whenever you'll get time, please create an acçount, even if it's fake, and do messàge me. Because I really don't want to burden anyone with my messàges to móderators, or spàmming answers.

Please, please, please do messàge me in that, I'm really eager to talk to you after so many days!

Please rèport this answer.