Express the vector in the form \( a i+b j+ \) ck. \( \overrightarrow{P_{1} P_{2}} \) if \( P_{1} \) is the point \( (3,3,4) \) and \( P_{2} \) is the point \( (5,0,0) \) \( v=-2 i+3 j-4 k \) \( v=-2 i
Jadybug5885
To express the vector \( \overrightarrow{P_{1} P_{2}} \) in the form \( a i+b j+ ck \), we can subtract the coordinates of \( P_{1} \) from the coordinates of \( P_{2} \) and then multiply each component by the respective unit vector.
First, subtract the coordinates:
\( P_{2} - P_{1} = (5,0,0) - (3,3,4) = (2,-3,-4) \)
Now, multiply each component by the respective unit vector:
\( (2,-3,-4) = 2i - 3j - 4k \)
So, the vector \( \overrightarrow{P_{1} P_{2}} \) can be expressed in the form \( 2i - 3j - 4k \).
To express the vector \( \overrightarrow{P_{1} P_{2}} \) in the form \( a i+ b j+ c k \), we will find the difference between the coordinates of point \( P_{2} \) and point \( P_{1} \), and then substitute those differences into the equation.
Given:
Point \( P_{1} \) coordinates: (3, 3, 4)
Point \( P_{2} \) coordinates: (5, 0, 0)
To find \( \overrightarrow{P_{1} P_{2}} \):
1. Subtract the x-coordinates: \( 5 - 3 = 2 \)
2. Subtract the y-coordinates: \( 0 - 3 = -3 \)
3. Subtract the z-coordinates: \( 0 - 4 = -4 \)
Therefore, \( \overrightarrow{P_{1} P_{2}} = 2i - 3j - 4k \).
I noticed that you also mentioned the vector \( v = -2i + 3j - 4k \). If you have any specific questions or if there is anything else you would like to know, please let me know!