Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of vector PQ . (1 point) <2, 5>, square root of twenty nine <-2, -5>, 29 <2, 5>, 2…

Question

asked Apr 16, 2022 169k views

1 Answer

Haoyu Chen · Answer 1 · 2022-04-22T14:06:37+0000

Given:

The two endpoints of a vector are P = (2, 9) and Q = (4, 14).

To find:

The component form and magnitude of vector PQ .

Solution:

A vector is defined as

$v=\left<x_2-x_1,y_2-y_1\right>$

Where,
(x_1,y_1) is the initial point and
(x_2,y_2) is the terminal point.

Two endpoints of a vector are P = (2, 9) and Q = (4, 14). So, the vector PQ is

$\overrightarrow{PQ}=\left<4-2,14-9\right>$

$\overrightarrow{PQ}=\left<2,5\right>$

Component form of vector PQ is
$\left<2,5\right>$ .

The magnitude of a vector
$v=\left<a,b\right>$ is

$|\vec{v}|=√(a^2+b^2)$

The magnitude of vector PQ is:

$|\overrightarrow{PQ}|=√(2^2+5^2)$

$|\overrightarrow{PQ}|=√(4+25)$

$|\overrightarrow{PQ}|=√(29)$

Therefore, the correct option is A.