If vec{A} + vec{B} = vec{C} and A + B = C,wha | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The magnitude of the resultant vector $\vec{C} = \vec{A} + \vec{B}$ is given by the formula $C = \sqrt{A^2 + B^2 + 2AB \cos 	heta}$,where $	heta

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) The magnitude of the resultant vector $\vec{C} = \vec{A} + \vec{B}$ is given by the formula $C = \sqrt{A^2 + B^2 + 2AB \cos 	heta}$,where $	heta$ is the angle between $\vec{A}$ and $\vec{B}$.Given that $C = A + B$,we substitute this into the equation:$A + B = \sqrt{A^2 + B^2 + 2AB \cos 	heta}$Squaring both sides:$(A + B)^2 = A^2 + B^2 + 2AB \cos 	heta$$A^2 + B^2 + 2AB = A^2 + B^2 + 2AB \cos 	heta$Subtracting $A^2 + B^2$ from both sides:$2AB = 2AB \cos 	heta$Assuming $A, B 
eq 0$,we divide by $2AB$:$1 = \cos 	heta$Therefore,$	heta = 0$.

If $\vec{A} + \vec{B} = \vec{C}$ and $A + B = C$,what is the angle between $\vec{A}$ and $\vec{B}$?

Similar Questions

What is the meaning of subtraction of two vectors?

If the magnitudes of vectors $\vec P$,$\vec Q$,and $\vec R$ are $5$,$12$,and $13$ units respectively,and if $\vec P + \vec Q = \vec R$,then the angle between $\vec Q$ and $\vec R$ is:

The figure shows three vectors $p$,$q$,and $r$,where $C$ is the midpoint of $AB$. Which of the following relations is correct?

Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are in the ratio $3:1.$ Which of the following relations is true?

Which vector must be added to the resultant vector $\vec{P} = 2\hat{i} + 7\hat{j} - 10\hat{k}$ and $\vec{Q} = \hat{i} + 2\hat{j} + 3\hat{k}$ to obtain a unit vector along the $X$-axis?

Vedclass Test Series

Exam Paper Generator

Online Exam Module