Let overrightarrow C = overrightarrow A + ove | vedclass

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

Question

(A) The magnitude of the resultant vector $\overrightarrow C = \overrightarrow A + \overrightarrow B$ is given by $|\overrightarrow C| = \sqrt{|\overr

Vedclass · Accepted Answer

$A$ and $C$

Vedclass · Answer

(A) The magnitude of the resultant vector $\overrightarrow C = \overrightarrow A + \overrightarrow B$ is given by $|\overrightarrow C| = \sqrt{|\overrightarrow A|^2 + |\overrightarrow B|^2 + 2|\overrightarrow A||\overrightarrow B| \cos 	heta}$,where $	heta$ is the angle between $\overrightarrow A$ and $\overrightarrow B$.Statement $(A)$: If $\overrightarrow A$ and $\overrightarrow B$ are vectors such that their sum $\overrightarrow C$ has a smaller magnitude than both,it is possible if the angle between them is obtuse (specifically,$90^\circ Statement $(B)$: This is incorrect because if $\overrightarrow B$ is a null vector or if the angle $	heta$ is such that the resultant magnitude decreases,$|\overrightarrow C|$ can be less than or equal to $|\overrightarrow A|$.Statement $(C)$: If $\overrightarrow A$ and $\overrightarrow B$ are in the same direction $(	heta = 0^\circ)$,then $|\overrightarrow C| = |\overrightarrow A| + |\overrightarrow B|$. Thus,$(C)$ is correct.Statement $(D)$: This is the negation of $(C)$ and is therefore incorrect.Since $(A)$ and $(C)$ are correct,the correct option is $A$.

Similar Questions

$A$ vector $\overrightarrow{A}$ when added to the sum of the vectors $(\hat{\imath}-2 \hat{\jmath}+2 \hat{k})$ and $(-2 \hat{\imath}+\hat{\jmath}-\hat{k})$ gives a unit vector along the $y$-axis. The magnitude of the vector $\overrightarrow{A}$ is

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

Among the given pairs of vectors,the resultant of two vectors can never be $3$ units. The vectors are

Given $|\vec{P}| > |\vec{Q}|$. What is the angle between their maximum resultant vector and minimum resultant vector (in $^{\circ}$)?

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is . . . . . . (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module