Question

Vector Vector P Q has an initial point at (3, 3) and its terminal point is at (5, 7).
Vector Vector R S has an initial point at (4, –6) and its terminal point is at (1, –5).
What is the component form of vector ?

The correct answer is: 5,3

Answer 1

Initial and terminal points of the vector $\vec{PQ}$ of (3., 3) and (5, 7) , and the initial and final point of the vector $\vec{RS}$ of (4, -5), and (1, -5), indicate that  the the difference between the vectors is; 5·i + 5·j

What is a vector?

A vector is a quantity that has both magnitude and direction.

The specified vectors are;

The initial and terminal point on vector $\vec{PQ}$ are; (3, 3) and (5, 7)
The initial and terminal point of vector  $\vec{RS}$ are  (4, -6), and (1, -5)

Therefore, the vector  $\vec{PQ}$ - $\vec{RS}$ is therefore;

The vector form of $\vec{PQ}$ = <5 - 3, 7 - 3> = <2, 4>

The vecror form of    $\vec{RS}$  = <1-4, -5 - (-6)> = <-3, -1>

The difference  between the vectors is therefore;

The vectors are therefore;

$\vec{PQ}$ = 2·i + 4·j

$\vec{RS}$ = -3·i - j

The difference between the vectors is therefore;

$\vec{PQ}$ - $\vec{RS}$ = (2 - (-3))·i + (4 - (-1))·j = 5·i + 5·j

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