If (p = begin{pmatrix} 2 \ -2 end{pmatrix} ) and (q = begin{pmatrix} 3 \ 4 end{pmatrix}), find (|q – frac{1}{2}p|).
-
A.
(2sqrt{2}) -
B.
(sqrt{13}) -
C.
(5) -
D.
(sqrt{29})
Correct Answer: Option D
Explanation
(p = begin{pmatrix} 2 \ -2 end{pmatrix} , q = begin{pmatrix} 3 \ 4 end{pmatrix})
(frac{1}{2}p = begin{pmatrix} 1 \ -1 end{pmatrix})
(q – frac{1}{2}p = begin{pmatrix} 3 \ 4 end{pmatrix} – begin{pmatrix} 1 \ -1 end{pmatrix} = begin{pmatrix} 2 \ 5 end{pmatrix})
(|q – frac{1}{2}p| = sqrt{2^{2} + 5^{2}} = sqrt{29})