A vector has a magnitude the same as that of | vedclass

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

Question

(A) First,calculate the magnitude of vector $\overrightarrow{A} = 3 \hat{i} + 4 \hat{j}$.$|\overrightarrow{A}| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \s

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) First,calculate the magnitude of vector $\overrightarrow{A} = 3 \hat{i} + 4 \hat{j}$.$|\overrightarrow{A}| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.Next,find the unit vector in the direction of $\overrightarrow{B} = 4 \hat{i} + 3 \hat{j}$.$|\overrightarrow{B}| = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = 5$.$\hat{B} = \frac{\overrightarrow{B}}{|\overrightarrow{B}|} = \frac{4 \hat{i} + 3 \hat{j}}{5}$.The required vector $\overrightarrow{V}$ has magnitude $5$ and is parallel to $\overrightarrow{B}$,so $\overrightarrow{V} = |\overrightarrow{A}| \hat{B} = 5 	imes \frac{4 \hat{i} + 3 \hat{j}}{5} = 4 \hat{i} + 3 \hat{j}$.Comparing this with the given components $X \hat{i} + 3 \hat{j}$,we find $X = 4$.

$A$ vector has a magnitude the same as that of $\overrightarrow{A} = 3 \hat{i} + 4 \hat{j}$ and is parallel to $\overrightarrow{B} = 4 \hat{i} + 3 \hat{j}$. The $x$ and $y$ components of this vector in the first quadrant are $X$ and $3$ respectively,where $X = $ . . . . . . .

Similar Questions

The angles which a vector $\hat{i} + \hat{j} + \sqrt{2} \hat{k}$ makes with $X, Y$ and $Z$ axes respectively are

What is the minimum number of coplanar vectors of different magnitudes whose sum can be zero?

$A$ mosquito is moving with a velocity $\overrightarrow{v} = 0.5t^2 \hat{i} + 3t \hat{j} + 9 \hat{k} \, m/s$. What will be the direction of the mosquito after $t = 2 \, s$?

The vector $\overrightarrow{OA}$ where $O$ is the origin is given by $\overrightarrow{OA} = 2\hat{i} + 2\hat{j}$. If it is rotated by $45^{\circ}$ in the anticlockwise direction about $O$,what will be the new vector?

If water at $100^\circ C$ cools in $10$ minutes to $80^\circ C$ and to $65^\circ C$ in the next $10$ minutes, then the room temperature will be ...

Vedclass Test Series

Exam Paper Generator

Online Exam Module