Question

Vector A⃗ points in the positive y direction and has a magnitude of 12 m. Vector B⃗ has a magnitude of 33 m and points in the negative x direction.
Find the direction of A⃗ + B⃗ .
Find the magnitude of A⃗ + B⃗ .

Answer 1

direction is neg x

mag is 21m

Answer 2

Answer:

The magnitude and direction of A+B is 35.11 and -19.98°

Explanation:

Given that,

Magnitude of vector A= 12j m

Magnitude of vector B = -33i m

We need to calculate the magnitude of |A+B|

$|A+B|=\sqrt{A^2+B^2}$

$|A+B|=\sqrt{(12)^2+(-33)^2}$

$|A+B|=35.11$

We need to calculate the direction of A+B

$\theta=tan^{-1}\dfrac{A}{B}$

$\theta=tan^{-1}\dfrac{12}{-33}$

$\theta=-19.98^{\circ}$

The direction is negative x - axis.

Hence, The magnitude and direction of A+B is 35.11 and -19.98°