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

The projection of vector $\vec{A}$ on $\vec{B}$ is:

Given $\vec{P} + \vec{Q} = \vec{P} - \vec{Q}$. Under what condition is this true?

$A$ physical quantity which has a direction:

If $\overrightarrow{A}$ is a vector with magnitude $(3, 4)$,show that the magnitude of its unit vector is $1$.

$A$ vector has magnitude and direction. Does it have a location in space? Can it vary with time? Will two equal vectors $a$ and $b$ at different locations in space necessarily have identical physical effects? Give examples in support of your answer.

Vedclass Test Series

Exam Paper Generator

Online Exam Module