find the magnitude of the resultant vector.\n(14, 7) |→r| = ?\n(-9, -2)\nround to the nearest hundredth.
find the magnitude of the resultant vector.\n(14, 7) |→r| = ?\n(-9, -2)\nround to the nearest hundredth.
Answer
Explanation:
Step1: Find the resultant vector components
To find the resultant vector (\vec{R}), we add the corresponding components of (\vec{v} = (14, 7)) and (\vec{w} = (-9, -2)). The (x)-component of (\vec{R}) is (14 + (-9)=14 - 9 = 5). The (y)-component of (\vec{R}) is (7+(-2)=7 - 2 = 5). So, (\vec{R}=(5,5)).
Step2: Calculate the magnitude of the resultant vector
The magnitude of a vector ((x,y)) is given by the formula (\vert\vec{R}\vert=\sqrt{x^{2}+y^{2}}). For (\vec{R}=(5,5)), we substitute (x = 5) and (y = 5) into the formula: (\vert\vec{R}\vert=\sqrt{5^{2}+5^{2}}=\sqrt{25 + 25}=\sqrt{50}) Simplify (\sqrt{50}\approx7.07) (rounded to the nearest hundredth).
Answer:
(7.07)