Question

If the magnitudes of two vectors are A and 2A and the angle between the two is 60°. The resultant of
the two vectors makes an angle
with A.​

Answer 1

Answer:

Ques 44: The angle between the two vectors (a) 60° (b) 0° (c) 90° (d) None of these Ans: 90° Sol: = 0 ⇒ θ = 90° Option (c) is correct. Ques 45: Maximum and minimum values of the resultant of two forces acting at a point are 7 N and 3 N respectively.

Explanation:

Answer 2

The angle made by the resultant vector with A vector is 41°.

Given:

The magnitudes of the two vectors are A and 2A.

The angle between the two vectors is 60°.

To Find:

The angle made by the resultant vector with A vector.

Solution:

We are required to find the angle made by the resultant vector with the A vector.

Let ϕ be the angle made by the resultant vector with vector A

From the picture given below

tanϕ = opposite side/adjacent side

tanϕ = 2A sinθ/(A+2Acosθ)   ------(1)

θ = 60°    (angle between two vectors)

Substitute the values of θ in the equation(1) we get

tanϕ = 2Asin60°/(A+2Acos60°)

tanϕ = $\frac{2A\frac{(\sqrt{3}}{2})}{A+2A(\frac{1}{2} )}$

tanϕ = √3A/(A+A)

tanϕ = √3A/2A

tanϕ = √3/2

ϕ = tan⁻¹(√3/2)

ϕ = tan⁻¹(0.8660)

ϕ = 41°

Therefore, The angle made by the resultant vector with A vector is 41°.

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