# Question #4dd1c

c

#### Explanation:

Draw 2 triangles from the vectors
vector a is 12m @ 40 degrees
vector b is 9m @ 20 degrees

Any line that's not straight can be a hypotnuse.
Based on the graph, you need cosine to find x since cos=hyp/adj and adj is moving in the x axis.

$\cos \theta = \frac{a \mathrm{dj}}{h y p}$ ---> $h y p \cos \theta = o p p$

Vector a: $a = 12 \cos 40 = 9.19$
Vector b: $b = 9 \cos 20 = 8.46$

a goes in the positive direction and b goes in the negative direction, so $9.19 - 8.46 = .735$ which is basically c

Mar 27, 2017

As given in the question

$\vec{a}$ subtends ${40}^{\circ}$ angle with +ve direction of X-axis and $\left\mid \vec{a} \right\mid = 12 m$

$\vec{b}$ subtends ${\left(180 - 20\right)}^{\circ} = {160}^{\circ}$ angle with +ve direction of X-axis and $\left\mid \vec{b} \right\mid = 9 m$

So the component of $\vec{a} + \vec{b}$ along X-axis will have magnitude

$= \left\mid \vec{a} \right\mid \cos {40}^{\circ} + \left\mid \vec{b} \right\mid \cos {160}^{\circ}$

$= \left(12 \cos {40}^{\circ} + 9 \cos {160}^{\circ}\right) m \approx 0.73 m$