Given that (AB = begin{pmatrix} 4 \ 3 end{pmatrix}) and (AC = begin{pmatrix} 2 \ -3 end{pmatrix}), find |BC|.
-
A.
(4sqrt{2}) -
B.
(6sqrt{2}) -
C.
(2sqrt{10}) -
D.
(4sqrt{10})
Correct Answer: Option C
Explanation
(BC = BA + AC)
Given, (AB), then (BA = – AB)
= (AB = begin{pmatrix} 4 \ 3 end{pmatrix} implies BA = begin{pmatrix} -4 \ -3 end{pmatrix})
(therefore BC = begin{pmatrix} -4 \ -3 end{pmatrix} + begin{pmatrix} 2 \ -3 end{pmatrix})
= (begin{pmatrix} -2 \ -6 end{pmatrix})
(|BC| = sqrt{(-2)^{2} + (-6)^{2}} = sqrt{40} )
= (2sqrt{10})