The component of vector overrightarrow{A}=a_x | vedclass

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

Question

(C) Let $\overrightarrow{B} = \hat{i} - \hat{j}$.To find the component of vector $\overrightarrow{A}$ along the direction of $\overrightarrow{B}$,we c

Vedclass · Accepted Answer

$(a_x-a_y) / \sqrt{2}$

Vedclass · Answer

(C) Let $\overrightarrow{B} = \hat{i} - \hat{j}$.To find the component of vector $\overrightarrow{A}$ along the direction of $\overrightarrow{B}$,we calculate the scalar projection of $\overrightarrow{A}$ onto the unit vector of $\overrightarrow{B}$.The unit vector along $\overrightarrow{B}$ is $\hat{b} = \frac{\overrightarrow{B}}{|\overrightarrow{B}|} = \frac{\hat{i} - \hat{j}}{\sqrt{1^2 + (-1)^2}} = \frac{\hat{i} - \hat{j}}{\sqrt{2}}$.The component of $\overrightarrow{A}$ along $\overrightarrow{B}$ is given by $\overrightarrow{A} \cdot \hat{b}$.$\overrightarrow{A} \cdot \hat{b} = (a_x \hat{i} + a_y \hat{j} + a_z \hat{k}) \cdot \left( \frac{\hat{i} - \hat{j}}{\sqrt{2}} \right)$.$= \frac{a_x(1) + a_y(-1) + a_z(0)}{\sqrt{2}} = \frac{a_x - a_y}{\sqrt{2}}$.

The component of vector $\overrightarrow{A}=a_x \hat{i}+a_y \hat{j}+a_z \hat{k}$ along the direction of $\hat{i}-\hat{j}$ is

Similar Questions

$A$ vector $\overrightarrow{A}$ makes equal angles with the $x$,$y$,and $z$ axes. Find the magnitude of its components.

The angles made by the vector $\vec{A} = 2\hat{i} + 3\hat{j}$ with the $x$-axis and the $y$-axis are respectively:

What is the maximum number of components into which a vector can be resolved?

Find the magnitude and direction of the vectors $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$. What are the components of a vector $\vec{A}=2\hat{i}+3\hat{j}$ along the directions of $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$?

Explain the resolution of vectors.

Vedclass Test Series

Exam Paper Generator

Online Exam Module