Question

Wo vectors a and b of magnitude 3 units and 4 units respectively make an angle 60 degree with each other. a) find the magnitude and the direction of the resultant vector.

Answer 1

Answer :

Two vectors A and B of magnitude 3 units and 4 units are inclined at angle 60°.

We have to find magnitude and direction of the resultant vector$.$

★ By parallelogram law of vector addition, the magnitude of resultant R at two vectors A and B inclined to each other at angle θ, is given by

• R² = A² + B² + 2AB cosθ

By substituting the given values,

➝ R² = 3² + 4² + 2(3)(4)cos60°

➝ R² = 25 + (24 × √3/2)

➝ R² = 25 + 12√3

➝ R² = 45.76

➝ R = 6.76 N

Direction of the resultant vector :

If resultant R makes an angle β with A then

• tan β = Bsinθ/(A + Bcosθ)

➝ tan β = 4sin60°/(3 + 4cos60°)

➝ tan β = (4√3/2)/(3 + 4/2)

➝ tan β = 2√3/(3+2)

➝ tan β = 2√3/5

➝ tan β = 0.692

➝ β = 34.68°