Answer:
Given vector v is,
[tex]\vec{v}=-24\vec{i}-7\vec{j}[/tex]
$=-24\vec{i}-7\vec{j}$To find the unit vector that has the same direction as the vector v is,
Unit vector u is,
[tex]\vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert}-----(1)[/tex]
we have that,
To find a unit vector with the same direction as a given vector, we divide the vector by its magnitude.
The magnitude of a vector formula is used to calculate the length of a vector and is denoted by |v|. The magnitude of a vector is always a positive number or zero it cannot be a negative number.
[tex]\lvert x\vec{i}+y\vec{j}\rvert=\sqrt[]{x^2+y^2}[/tex]
we get,
[tex]\lvert\vec{v}\rvert=\sqrt[]{24^2+7^2}[/tex][tex]=\sqrt[]{625}[/tex][tex]=25[/tex][tex]\lvert\vec{v}\rvert=25[/tex]
Substitute the values in equation (1), we get
[tex]\vec{u}=\frac{-24\vec{i}-7\vec{j}}{25}[/tex][tex]\vec{u}=\frac{1}{25}(-24\vec{i}-7\vec{j})[/tex]
Answer is:
[tex]\vec{u}=\frac{1}{25}(-24\vec{i}-7\vec{j})[/tex]
