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

vector A has magnitude 12 m and direction +y

so we can say

`\vec A = 12 \hat j`

vector B has magnitude 33 m and direction - x

`\vec B = -33 \hat i`

Now the resultant of vector A and B is given as

`\vec A + \vec B = 12 \hat j - 33 \hat i`

now for direction of the two vectors resultant will be given as

`\theta = tan^(-1)(12)/(-33)`

`\theta = 160 degree`

so it is inclined at 160 degree counterclockwise from + x axis

magnitude of A and B will be

`R = √(A^2 + B^2)`

`R = √(12^2 + 33^2) = 35.11 m`

so magnitude will be 35.11 m