Question

what is the length (magnitude) of the vector (6,-3)? a. √53 b. 3 c. √2 d. 3√5

Explanation:

Step1: Recall vector magnitude formula

For vector $(x,y)$, magnitude = $\sqrt{x^2 + y^2}$

Step2: Substitute vector components

$\sqrt{6^2 + (-3)^2} = \sqrt{36 + 9}$

Step3: Simplify the expression

$\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}$

Answer:

D. $3\sqrt{5}$