Question

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>, 29 <-2, -5>, square root of twenty nine

Answer 1

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

$|\vec{v}|=\sqrt{a^2+b^2}$

The magnitude of vector PQ is:

$|\overrightarrow{PQ}|=\sqrt{2^2+5^2}$

$|\overrightarrow{PQ}|=\sqrt{4+25}$

$|\overrightarrow{PQ}|=\sqrt{29}$

Therefore, the correct option is A.