First slide

Motion in a plane

Question

Two vectors $\vec{a}$ and $\vec{b}$ have equal magnitudes of 12 units. These vectors are making angles 30^o and 120^o with the x axis respectively. Their sum is $\vec{r}$ . Find the x and y components of $\vec{r}$ .

Moderate

A

$\large (6\sqrt 3 - 6),(6 + 6\sqrt 3 )$
B

$\large (6\sqrt 3 + 6),(6 + 6\sqrt 3 )$
C

$\large (6\sqrt 3 - 6),(6 - 6\sqrt 3 )$
D

$\large (6\sqrt 3 + 6),(6 - 6\sqrt 3 )$

Solution

Here a = b =12 units
X-component = a cos30⁰ – b cos60⁰
Y-component = a sin30⁰ + bsin 60⁰

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