Question

VECTORS
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 F. Find the x and y components of i​

Answer 1

Correct 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 r. Find the x and y components of r.

Answer:-

$\red{\bigstar}$ X component of r $\large\leadsto\boxed{\rm\purple{6(\sqrt{3}-1)}}$

$\red{\bigstar}$ Y component of r $\large\leadsto\boxed{\rm\purple{6(\sqrt{3}+1)}}$

• Solution:-

★ $\pink{\bf{Vector \: A:-}}$

Magnitude = 12 units

Angle = 30°

✧

→ $\sf A_x = 12 cos 30^{\circ}$

→ $\sf A_x = 12 \times \dfrac{\sqrt{3}}{2}$

→ $\bf A_x = 6 \sqrt{3} \hat{i}$

✧

→ $\sf A_y = 12 sin 30^{\circ}$

→ $\sf A_y = 12 \times \dfrac{1}{2}$

→ $\bf A_y = 6 \hat{j}$

$\large\boxed{\green{\vec{A} = 6\sqrt{3}\hat{i} + 6\hat{j}}}$

★ $\pink{\bf{Vector \: B:-}}$

Magnitude = 12 units

Angle = 120°

✧

→ $\sf B_x = 12 cos 120^{\circ}$

→ $\sf B_x = 12 \times \dfrac{-1}{2}$

→ $\bf B_x = -6 \hat{i}$

✧

→ $\sf B_y = 12 sin 120^{\circ}$

→ $\sf B_y = 12 \times \dfrac{\sqrt{3}}{2}$

→ $\bf B_y = 6 \sqrt{3}\hat{j}$

$\large\boxed{\green{\vec{B} = -6\hat{i} + 6\sqrt{3}\hat{j}}}$

★ $\pink{\bf{Vector \: R:-}}$

$\sf \vec{R} = \vec{A} + \vec{B}$

→ $\sf \vec{R} = (6\sqrt{3} \hat{i} + 6 \hat{j}) + (-6 \hat{i} + 6 \sqrt{3} \hat{j})$

→ $\large\boxed{\red{\vec{R} = 6(\sqrt{3} - 1) \hat{i} + 6(\sqrt{3} + 1) \hat{j}}}$

Therefore,

x component = 6(√3-1)

y component = 6(√3 + 1)