Question

Two vectors a and b have equal magnitudes of
12 units. These vectors are making angles 30°
and 120° with the x axis respectively. Their sum
is ř. Find the x and y components of r.
1) (673-6),(6+673)
2) (613+6),(6+673)
3) (673 – 6),(6-673)
4) (673+6),(6-673)​

Answer 1

Two vectors a and b have equal magnitudes of 12 units. These vectors are making angles 30° and 120° with the x axis respectively. Their sum is r. Find the x and y components of r.

magnitude of vector a = magnitude of vector b = 12 units.

vector a makes an angle 30° with x-axis.

so, a = 12(cos30° i + sin30° j)

= 12(√3/2 i + 1/2 j)

= 6√3 i + 6 j

again, vector b makes an angle 120° with x - axis .

so, b = 12(cos120° i + sin120°j)

= 12(-1/2 i + √3/2 j)

= -6 i + 6√3 j

a/c to question, r = a + b

so, r = (6√3 i + 6j) + (-6i + 6√3j)

= (6√3 - 6)i + (6 + 6√3)j

so, component of vector r along x-axis = (6√3 - 6)

so, component of vector r along x-axis = (6√3 - 6)and component of vector r along y-axis = (6 + √3)