The component of vector vec{A} = 2hat{i} + 3h | vedclass

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

Question

(A) The component of a vector $\vec{A}$ along the direction of a vector $\vec{B}$ is given by the scalar projection multiplied by the unit vector of $

Vedclass · Accepted Answer

$\frac{5}{\sqrt{2}}$

Vedclass · Answer

(A) The component of a vector $\vec{A}$ along the direction of a vector $\vec{B}$ is given by the scalar projection multiplied by the unit vector of $\vec{B}$,or simply the scalar projection if only the magnitude is asked. The question asks for the component (magnitude) of $\vec{A}$ along $\vec{B}$.Given $\vec{A} = 2\hat{i} + 3\hat{j}$ and $\vec{B} = \hat{i} + \hat{j}$.The scalar projection of $\vec{A}$ along $\vec{B}$ is given by $\frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}$.Calculate the dot product: $\vec{A} \cdot \vec{B} = (2)(1) + (3)(1) = 2 + 3 = 5$.Calculate the magnitude of $\vec{B}$: $|\vec{B}| = \sqrt{1^2 + 1^2} = \sqrt{2}$.Therefore,the component of $\vec{A}$ along $\vec{B}$ is $\frac{5}{\sqrt{2}}$.

The component of vector $\vec{A} = 2\hat{i} + 3\hat{j}$ along the vector $\vec{B} = \hat{i} + \hat{j}$ is:

Similar Questions

Which of the following is not an illustration of viscosity?

The unit vector $(a \hat{\imath} + b \hat{\jmath})$ is perpendicular to $(\hat{\imath} + \hat{\jmath})$. The value of $b$ is

What is the wave number of the lowest energy transition associated with the Paschen series?

In a regular octagon $ABCDEFGH$ with center $O$,what is the sum of $\overrightarrow{ AB }+\overrightarrow{ AC }+\overrightarrow{ AD }+\overrightarrow{ AE }+\overrightarrow{ AF }+\overrightarrow{ AG }+\overrightarrow{ AH }$ if $\overrightarrow{ AO }=2 \hat{ i }+3 \hat{ j }-4 \hat{ k }$?

There are two vectors $\vec{A} = 6\hat{i} + 9\hat{j} - \hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} - p\hat{k}$ which have the same direction. The value of '$p$' is

Vedclass Test Series

Exam Paper Generator

Online Exam Module