Answer to Question #279658 in Mechanics | Relativity for Mzizah

Question

d) The unit–vector notation of the two vectors a = 4.0i + 3.0j and b = −13.0i + 7.0j. Determine

the magnitude and direction of a + b [4mks

Answer 1

Sum of the vectors:

$a + b = (4.0 + (-13.0))i + (3.0 + 7.0)j = -9.0i + 10.0j$

Magnitude:

$|| a + b || = \sqrt{(-9.0)^2 + 10.0^2} \approx 13.45$

Direction:

$\tan(\theta) = \cfrac{10.0}{-9.0} \\ \theta = \tan^{-1} (\cfrac{10.0}{-9.0}) \approx 132.0 \degree$