Question

find a unit vector in the direction of the vector 3i+4j​

Answer 1

û = 3î + 4j / |3î + 4j|

û = 3î + 4j / 5

Answer 2

Answer:

Unit vector in the direction of the vector 3i+4j​ is $\frac{3}{5} i+\frac{4}{5} j$.

Explanation:

Step : 1  Given :  $\vec{V}=3 \hat{i}+4 \hat{j}$

$\therefore \quad \text$  { Magnitude of } $\vec{V}=|\vec{V}|=\sqrt{3^2+4^2}=\sqrt{25}=5$

$\text { Let } \overrightarrow{\mathrm{V}}=\hat{\alpha}|\overrightarrow{\mathrm{V}}| \text$   where $\hat{\alpha} \text$  is a unit vector along$\overrightarrow{\mathrm{V}}$

$\therefore \quad \hat{\alpha}=\frac{\vec{V}}{|\overrightarrow{\mathrm{V}}|}=\frac{3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}}{5}=\frac{3}{5} \hat{\mathrm{i}}+\frac{4}{5} \hat{\mathrm{j}}$

Required unit vector is  $\frac{3}{5} \hat{i}+\frac{4}{5} \hat{j} \text {. }$

Step : 2 As a result, the vector 3i + 4j has a 5 unit magnitude. The mathematical formula for this statement is: |3i+4j| = 5. (Vertical lines indicate magnitude.) A vector with a magnitude of one is referred to as a unit vector. Unit vectors are denoted by the "cap" sign (). The length of a unit vector is one. It is frequently used to describe the direction of a vector. For instance, A = 1 | A | A is how a unit vector for the vector A, A is defined.

Step : 3  A line of length 3 units can be used to generate a vector representation of the velocity vector A = 3i, which has a magnitude of 3 units/sec. Unit Vector = Vector/magnitude Vector's is the formula for a unit vector pointing in the direction of a given vector. |v| =(x2 + y2) is the formula to calculate the magnitude of a vector (in two dimensions) v = (x, y). The Pythagorean theorem serves as the basis for this formula. |V| = (x2 + y2 + z2) is the formula to calculate the magnitude of a vector (in three-dimensional space) V = (x, y, z).

To learn more about similar questions visit:

https://brainly.in/question/13994117?referrer=searchResults

https://brainly.in/question/12541272?referrer=searchResults

#SPJ3