Question

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

Answer 1

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 \( 2i - 3j - 4k \).