Question

) 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

Explanations & calculations

• Vector addition

$\qquad\qquad \begin{aligned} \small \vec{a}+\vec{b}&=\small 4i+3j+(-13i)+7j\\ &=\small -9i+10j \end{aligned}$

• Magnitude: consider the modulus

$\qquad\qquad \begin{aligned} \small |\vec{a}+\vec{b}|&=\small \sqrt{(-9)^2+10^2}\\ &=\small \sqrt{181}\\ &=\small 13.5 \end{aligned}$

• Direction

$\qquad\qquad \begin{aligned} \small \tan\theta&=\small \frac{10}{-9}\\ \small \theta&=\small -48.0^0 \end{aligned}$